```
----
4D
----
```

or by complexity (only including stary cases for quasiregular linear diagrams)
or by similarity.

### Terse Overview

Indepted to the mere quantity of cases the following overview table links to additional pages too; only parts are listed in details below.

 Linear Dynkin Graphs Tridental Dynkin Graphs Loop-n-Tail Dynkin Graphs Loop Dynkin Graphs Two-Loop Dynkin Graphs Simplical Dynkin Graphs Others ``` o-P-o-Q-o-R-o ``` ```o-P-o-Q-o *b-R-o = o_ -P_ >o---R---o _Q- o- ``` ```o-P-o-Q-o-R-o-S-*b = o_ | -Q_ R >o---P---o | _S- o- ``` ```o-P-o-Q-o-R-o-S-*a = o---P---o | | S Q | | o---R---o ``` ```o-P-o-Q-o-R-o-S-*a-T-*c = _o_ _P- | -S_ o< T >o -Q_ | _R- -o- ``` ```o-P-o-Q-o-R-o-S-*a-T-*c *b-U-*d = o / T \ P _o_ S /_Q R_\ o-----U-----o ```

In the following symmetry listings "etc." means replacments according to 33/2, to 44/3, to 55/4, or to 5/25/3.

Polychora with Grünbaumian elements so far are not investigated any further. Those are Grünbaumian a priori, usually because of some subgraph -x-n/d-x-, where d is even. Others, which come out as being Grünbaumian a posteriori will be given none the less.

*) not even a scaliform representation does exist, just occures as pure faceting
**) not uniform, but at least scaliform

 two-loop ones ```o-P-o-Q-o-R-o-S-*a-T-*c = _o_ _P- | -S_ o< T >o -Q_ | _R- -o- ```

### Demi-Tesseractic ("demi-tessic") Symmetries   (up)

 o3o3o3o3*a3/2*c (µ=2) o3o3/2o3/2o3*a3*c (µ=6) o3o3/2o3o3/2*a3*c (µ=10) quasiregulars ```x3o3o3o3*a3/2*c - (contains "2tet") o3x3o3o3*a3/2*c - (contains "2tet") ``` ```x3o3/2o3/2o3*a3*c - (contains "2tet") o3x3/2o3/2o3*a3*c - (contains "2tet") o3o3/2x3/2o3*a3*c - (contains "2tet") ``` ```x3o3/2o3o3/2*a3*c - (contains "2tet") o3x3/2o3o3/2*a3*c - (contains "2tet") ``` otherWythoffians ```x3x3o3o3*a3/2*c - (contains "2tet") x3o3x3o3*a3/2*c - [Grünbaumian] o3x3o3x3*a3/2*c - x3x3x3o3*a3/2*c - [Grünbaumian] x3x3o3x3*a3/2*c - rawvhitto x3x3x3x3*a3/2*c - [Grünbaumian] ``` ```x3x3/2o3/2o3*a3*c - (contains "2tet") x3o3/2x3/2o3*a3*c - "2oh" o3x3/2x3/2o3*a3*c - [Grünbaumian] o3x3/2o3/2x3*a3*c - x3x3/2x3/2o3*a3*c - [Grünbaumian] x3x3/2o3/2x3*a3*c - o3x3/2x3/2x3*a3*c - [Grünbaumian] x3x3/2x3/2x3*a3*c - [Grünbaumian] ``` ```x3x3/2o3o3/2*a3*c - (contains "2tet") x3o3/2x3o3/2*a3*c - "2oh" o3x3/2x3o3/2*a3*c - [Grünbaumian] o3x3/2o3x3/2*a3*c - x3x3/2x3o3/2*a3*c - [Grünbaumian] x3x3/2o3x3/2*a3*c - x3x3/2x3x3/2*a3*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o3o3/2o3/2*a3/2*c (µ=14) o3/2o3/2o3/2o3/2*a3/2*c (µ=34) quasiregulars ```x3o3o3/2o3/2*a3/2*c - (contains "2tet") o3x3o3/2o3/2*a3/2*c - (contains "2tet") o3o3o3/2x3/2*a3/2*c - (contains "2tet") ``` ```x3/2o3/2o3/2o3/2*a3/2*c - (contains "2tet") o3/2x3/2o3/2o3/2*a3/2*c - (contains "2tet") ``` otherWythoffians ```x3x3o3/2o3/2*a3/2*c - (contains "2tet") x3o3x3/2o3/2*a3/2*c - [Grünbaumian] x3o3o3/2x3/2*a3/2*c - [Grünbaumian] o3x3o3/2x3/2*a3/2*c - x3x3x3/2o3/2*a3/2*c - [Grünbaumian] x3x3o3/2x3/2*a3/2*c - [Grünbaumian] x3o3x3/2x3/2*a3/2*c - [Grünbaumian] x3x3x3/2x3/2*a3/2*c - [Grünbaumian] ``` ```x3/2x3/2o3/2o3/2*a3/2*c - [Grünbaumian] x3/2o3/2x3/2o3/2*a3/2*c - [Grünbaumian] o3/2x3/2o3/2x3/2*a3/2*c - x3/2x3/2x3/2o3/2*a3/2*c - [Grünbaumian] x3/2x3/2o3/2x3/2*a3/2*c - [Grünbaumian] x3/2x3/2x3/2x3/2*a3/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ```

### Icositetrachoral ("icoic") Symmetries   (up)

 o3o4o3o4*a4/3*c (µ=5) o3o4/3o3/2o4*a4*c (µ=19) o3/2o4o3/2o4*a4*c (µ=29) quasiregulars ```x3o4o3o4*a4/3*c - (contains "oct+6{4}","2cube") o3x4o3o4*a4/3*c - (contains "oct+6{4}") ``` ```x3o4/3o3/2o4*a4*c - (contains "oct+6{4}","2cube") o3x4/3o3/2o4*a4*c - (contains "oct+6{4}") o3o4/3x3/2o4*a4*c - (contains "oct+6{4}","2cube") o3o4/3o3/2x4*a4*c - (contains "oct+6{4}") ``` ```x3/2o4o3/2o4*a4*c - (contains "oct+6{4}","2cube") o3/2x4o3/2o4*a4*c - (contains "oct+6{4}") ``` otherWythoffians ```x3x4o3o4*a4/3*c - (contains "2cube",2cho) x3o4x3o4*a4/3*c - afdec x3o4o3x4*a4/3*c - (contains "oct+6{4}") o3x4o3x4*a4/3*c - x3x4x3o4*a4/3*c - ditdi x3x4o3x4*a4/3*c - x3x4x3x4*a4/3*c - croc ``` ```x3x4/3o3/2o4*a4*c - (contains "2cube",2cho) x3o4/3x3/2o4*a4*c - girfaddic x3o4/3o3/2x4*a4*c - (contains "oct+6{4}") o3x4/3x3/2o4*a4*c - (contains "oct+6{4}") o3x4/3o3/2x4*a4*c - o3o4/3x3/2x4*a4*c - [Grünbaumian] x3x4/3x3/2o4*a4*c - diquitdi x3x4/3o3/2x4*a4*c - x3o4/3x3/2x4*a4*c - [Grünbaumian] o3x4/3x3/2x4*a4*c - [Grünbaumian] x3x4/3x3/2x4*a4*c - [Grünbaumian] ``` ```x3/2x4o3/2o4*a4*c - [Grünbaumian] x3/2o4x3/2o4*a4*c - girfaddic x3/2o4o3/2x4*a4*c - (contains "oct+6{4}") o3/2x4o3/2x4*a4*c - x3/2x4x3/2o4*a4*c - [Grünbaumian] x3/2x4o3/2x4*a4*c - [Grünbaumian] x3/2x4x3/2x4*a4*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o4/3o3o4/3*a4*c (µ=77) o3o4o3/2o4/3*a4/3*c (µ=91) o3/2o4/3o3/2o4/3*a4/3*c (µ=245) quasiregulars ```x3o4/3o3o4/3*a4*c - (contains "oct+6{4}","2cube") o3x4/3o3o4/3*a4*c - (contains "oct+6{4}") ``` ```x3o4o3/2o4/3*a4/3*c - (contains "oct+6{4}","2cube") o3x4o3/2o4/3*a4/3*c - (contains "oct+6{4}") o3o4x3/2o4/3*a4/3*c - (contains "oct+6{4}","2cube") o3o4o3/2x4/3*a4/3*c - (contains "oct+6{4}") ``` ```x3/2o4/3o3/2o4/3*a4/3*c - (contains "oct+6{4}","2cube") o3/2x4/3o3/2o4/3*a4/3*c - (contains "oct+6{4}") ``` otherWythoffians ```x3x4/3o3o4/3*a4*c - (contains "2cube",2cho) x3o4/3x3o4/3*a4*c - girfaddic x3o4/3o3x4/3*a4*c - (contains "oct+6{4}") o3x4/3o3x4/3*a4*c - x3x4/3x3o4/3*a4*c - diquitdi x3x4/3o3x4/3*a4*c - x3x4/3x3x4/3*a4*c - coqroc ``` ```x3x4o3/2o4/3*a4/3*c - (contains "2cube",2cho) x3o4x3/2o4/3*a4/3*c - afdec x3o4o3/2x4/3*a4/3*c - (contains "oct+6{4}") o3x4x3/2o4/3*a4/3*c - (contains "oct+6{4}") o3x4o3/2x4/3*a4/3*c - o3o4x3/2x4/3*a4/3*c - [Grünbaumian] x3x4x3/2o4/3*a4/3*c - ditdi x3x4o3/2x4/3*a4/3*c - x3o4x3/2x4/3*a4/3*c - [Grünbaumian] o3x4x3/2x4/3*a4/3*c - [Grünbaumian] x3x4x3/2x4/3*a4/3*c - [Grünbaumian] ``` ```x3/2x4/3o3/2o4/3*a4/3*c - [Grünbaumian] x3/2o4/3x3/2o4/3*a4/3*c - afdec x3/2o4/3o3/2x4/3*a4/3*c - (contains "oct+6{4}") o3/2x4/3o3/2x4/3*a4/3*c - x3/2x4/3x3/2o4/3*a4/3*c - [Grünbaumian] x3/2x4/3o3/2x4/3*a4/3*c - [Grünbaumian] x3/2x4/3x3/2x4/3*a4/3*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o3o5*a3/2*c   (up)

 o3o3o3o5*a3/2*c (µ=7) o3o3/2o3/2o5*a3*c (µ=113) o3/2o3o3o5/4*a3*c (µ=593) o3/2o3o3/2o5*a3*c (µ=607) quasiregulars ```x3o3o3o5*a3/2*c - (contains "2tet") o3x3o3o5*a3/2*c - (contains "2tet") o3o3x3o5*a3/2*c - (contains "2tet") o3o3o3x5*a3/2*c - sidtaxady ``` ```x3o3/2o3/2o5*a3*c - (contains "2tet") o3x3/2o3/2o5*a3*c - (contains "2tet") o3o3/2x3/2o5*a3*c - (contains "2tet") o3o3/2o3/2x5*a3*c - sidtaxady ``` ```x3/2o3o3o5/4*a3*c - (contains "2tet") o3/2x3o3o5/4*a3*c - (contains "2tet") o3/2o3x3o5/4*a3*c - (contains "2tet") o3/2o3o3x5/4*a3*c - sidtaxady ``` ```x3/2o3o3/2o5*a3*c - (contains "2tet") o3/2x3o3/2o5*a3*c - (contains "2tet") o3/2o3x3/2o5*a3*c - (contains "2tet") o3/2o3o3/2x5*a3*c - sidtaxady ``` otherWythoffians ```x3x3o3o5*a3/2*c - stut dixady x3o3x3o5*a3/2*c - [Grünbaumian] x3o3o3x5*a3/2*c - (contains "2tet") o3x3x3o5*a3/2*c - (contains "2gike") o3x3o3x5*a3/2*c - o3o3x3x5*a3/2*c - (contains "2tet") x3x3x3o5*a3/2*c - [Grünbaumian] x3x3o3x5*a3/2*c - x3o3x3x5*a3/2*c - [Grünbaumian] o3x3x3x5*a3/2*c - sik vadixady x3x3x3x5*a3/2*c - [Grünbaumian] ``` ```x3x3/2o3/2o5*a3*c - stut dixady x3o3/2x3/2o5*a3*c - gefdit dixdy x3o3/2o3/2x5*a3*c - (contains "2tet") o3x3/2x3/2o5*a3*c - [Grünbaumian] o3x3/2o3/2x5*a3*c - o3o3/2x3/2x5*a3*c - [Grünbaumian] x3x3/2x3/2o5*a3*c - [Grünbaumian] x3x3/2o3/2x5*a3*c - x3o3/2x3/2x5*a3*c - [Grünbaumian] o3x3/2x3/2x5*a3*c - [Grünbaumian] x3x3/2x3/2x5*a3*c - [Grünbaumian] ``` ```x3/2x3o3o5/4*a3*c - [Grünbaumian] x3/2o3x3o5/4*a3*c - gefdit dixdy x3/2o3o3x5/4*a3*c - [Grünbaumian] o3/2x3x3o5/4*a3*c - (contains "2gike") o3/2x3o3x5/4*a3*c - o3/2o3x3x5/4*a3*c - (contains "2tet") x3/2x3x3o5/4*a3*c - [Grünbaumian] x3/2x3o3x5/4*a3*c - [Grünbaumian] x3/2o3x3x5/4*a3*c - [Grünbaumian] o3/2x3x3x5/4*a3*c - x3/2x3x3x5/4*a3*c - [Grünbaumian] ``` ```x3/2x3o3/2o5*a3*c - [Grünbaumian] x3/2o3x3/2o5*a3*c - gefdit dixdy x3/2o3o3/2x5*a3*c - (contains "2tet") o3/2x3x3/2o5*a3*c - (contains "2gike") o3/2x3o3/2x5*a3*c - o3/2o3x3/2x5*a3*c - [Grünbaumian] x3/2x3x3/2o5*a3*c - [Grünbaumian] x3/2x3o3/2x5*a3*c - [Grünbaumian] x3/2o3x3/2x5*a3*c - [Grünbaumian] o3/2x3x3/2x5*a3*c - [Grünbaumian] x3/2x3x3/2x5*a3*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o3/2o3o5*a3/2*c (µ=713) o3o3/2o3o5/4*a3*c (µ=1087) o3o3o3/2o5/4*a3/2*c (µ=1193) o3/2o3/2o3/2o5/4*a3/2*c (µ=2887) quasiregulars ```x3/2o3/2o3o5*a3/2*c - (contains "2tet") o3/2x3/2o3o5*a3/2*c - (contains "2tet") o3/2o3/2x3o5*a3/2*c - (contains "2tet") o3/2o3/2o3x5*a3/2*c - sidtaxady ``` ```x3o3/2o3o5/4*a3*c - (contains "2tet") o3x3/2o3o5/4*a3*c - (contains "2tet") o3o3/2x3o5/4*a3*c - (contains "2tet") o3o3/2o3x5/4*a3*c - sidtaxady ``` ```x3o3o3/2o5/4*a3/2*c - (contains "2tet") o3x3o3/2o5/4*a3/2*c - (contains "2tet") o3o3x3/2o5/4*a3/2*c - (contains "2tet") o3o3o3/2x5/4*a3/2*c - sidtaxady ``` ```x3/2o3/2o3/2o5/4*a3/2*c - (contains "2tet") o3/2x3/2o3/2o5/4*a3/2*c - (contains "2tet") o3/2o3/2x3/2o5/4*a3/2*c - (contains "2tet") o3/2o3/2o3/2x5/4*a3/2*c - sidtaxady ``` otherWythoffians ```x3/2x3/2o3o5*a3/2*c - [Grünbaumian] x3/2o3/2x3o5*a3/2*c - [Grünbaumian] x3/2o3/2o3x5*a3/2*c - (contains "2tet") o3/2x3/2x3o5*a3/2*c - [Grünbaumian] o3/2x3/2o3x5*a3/2*c - o3/2o3/2x3x5*a3/2*c - (contains "2tet") x3/2x3/2x3o5*a3/2*c - [Grünbaumian] x3/2x3/2o3x5*a3/2*c - [Grünbaumian] x3/2o3/2x3x5*a3/2*c - [Grünbaumian] o3/2x3/2x3x5*a3/2*c - [Grünbaumian] x3/2x3/2x3x5*a3/2*c - [Grünbaumian] ``` ```x3x3/2o3o5/4*a3*c - stut dixady x3o3/2x3o5/4*a3*c - gefdit dixdy x3o3/2o3x5/4*a3*c - [Grünbaumian] o3x3/2x3o5/4*a3*c - [Grünbaumian] o3x3/2o3x5/4*a3*c - o3o3/2x3x5/4*a3*c - (contains "2tet") x3x3/2x3o5/4*a3*c - [Grünbaumian] x3x3/2o3x5/4*a3*c - [Grünbaumian] x3o3/2x3x5/4*a3*c - [Grünbaumian] o3x3/2x3x5/4*a3*c - [Grünbaumian] x3x3/2x3x5/4*a3*c - [Grünbaumian] ``` ```x3x3o3/2o5/4*a3/2*c - stut dixady x3o3x3/2o5/4*a3/2*c - [Grünbaumian] x3o3o3/2x5/4*a3/2*c - [Grünbaumian] o3x3x3/2o5/4*a3/2*c - (contains "2gike") o3x3o3/2x5/4*a3/2*c - o3o3x3/2x5/4*a3/2*c - [Grünbaumian] x3x3x3/2o5/4*a3/2*c - [Grünbaumian] x3x3o3/2x5/4*a3/2*c - [Grünbaumian] x3o3x3/2x5/4*a3/2*c - [Grünbaumian] o3x3x3/2x5/4*a3/2*c - [Grünbaumian] x3x3x3/2x5/4*a3/2*c - [Grünbaumian] ``` ```x3/2x3/2o3/2o5/4*a3/2*c - [Grünbaumian] x3/2o3/2x3/2o5/4*a3/2*c - [Grünbaumian] x3/2o3/2o3/2x5/4*a3/2*c - [Grünbaumian] o3/2x3/2x3/2o5/4*a3/2*c - [Grünbaumian] o3/2x3/2o3/2x5/4*a3/2*c - o3/2o3/2x3/2x5/4*a3/2*c - [Grünbaumian] x3/2x3/2x3/2o5/4*a3/2*c - [Grünbaumian] x3/2x3/2o3/2x5/4*a3/2*c - [Grünbaumian] x3/2o3/2x3/2x5/4*a3/2*c - [Grünbaumian] o3/2x3/2x3/2x5/4*a3/2*c - [Grünbaumian] x3/2x3/2x3/2x5/4*a3/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3/2o3o3o5/2*a3*c   (up)

 o3/2o3o3o5/2*a3*c (µ=103) o3o3/2o3o5/2*a3*c (µ=137) o3o3o3o5/3*a3/2*c (µ=497) o3o3o3/2o5/2*a3/2*c (µ=703) quasiregulars ```x3/2o3o3o5/2*a3*c - (contains "2tet") o3/2x3o3o5/2*a3*c - (contains "2tet") o3/2o3x3o5/2*a3*c - (contains "2tet") o3/2o3o3x5/2*a3*c - gardtaxady ``` ```x3o3/2o3o5/2*a3*c - (contains "2tet") o3x3/2o3o5/2*a3*c - (contains "2tet") o3o3/2x3o5/2*a3*c - (contains "2tet") o3o3/2o3x5/2*a3*c - gardtaxady ``` ```x3o3o3o5/3*a3/2*c - (contains "2tet") o3x3o3o5/3*a3/2*c - (contains "2tet") o3o3x3o5/3*a3/2*c - (contains "2tet") o3o3o3x5/3*a3/2*c - gardtaxady ``` ```x3o3o3/2o5/2*a3/2*c - (contains "2tet") o3x3o3/2o5/2*a3/2*c - (contains "2tet") o3o3x3/2o5/2*a3/2*c - (contains "2tet") o3o3o3/2x5/2*a3/2*c - gardtaxady ``` otherWythoffians ```x3/2x3o3o5/2*a3*c - [Grünbaumian] x3/2o3x3o5/2*a3*c - sefdit dixdy x3/2o3o3x5/2*a3*c - [Grünbaumian] o3/2x3x3o5/2*a3*c - (contains "2ike") o3/2x3o3x5/2*a3*c - o3/2o3x3x5/2*a3*c - (contains "2tet") x3/2x3x3o5/2*a3*c - [Grünbaumian] x3/2x3o3x5/2*a3*c - [Grünbaumian] x3/2o3x3x5/2*a3*c - [Grünbaumian] o3/2x3x3x5/2*a3*c - gik vadixady x3/2x3x3x5/2*a3*c - [Grünbaumian] ``` ```x3x3/2o3o5/2*a3*c - getit dixady x3o3/2x3o5/2*a3*c - sefdit dixdy x3o3/2o3x5/2*a3*c - [Grünbaumian] o3x3/2x3o5/2*a3*c - [Grünbaumian] o3x3/2o3x5/2*a3*c - o3o3/2x3x5/2*a3*c - (contains "2tet") x3x3/2x3o5/2*a3*c - [Grünbaumian] x3x3/2o3x5/2*a3*c - [Grünbaumian] x3o3/2x3x5/2*a3*c - [Grünbaumian] o3x3/2x3x5/2*a3*c - [Grünbaumian] x3x3/2x3x5/2*a3*c - [Grünbaumian] ``` ```x3x3o3o5/3*a3/2*c - getit dixady x3o3x3o5/3*a3/2*c - [Grünbaumian] x3o3o3x5/3*a3/2*c - (contains "2tet") o3x3x3o5/3*a3/2*c - (contains "2ike") o3x3o3x5/3*a3/2*c - o3o3x3x5/3*a3/2*c - (contains "2tet") x3x3x3o5/3*a3/2*c - [Grünbaumian] x3x3o3x5/3*a3/2*c - x3o3x3x5/3*a3/2*c - [Grünbaumian] o3x3x3x5/3*a3/2*c - x3x3x3x5/3*a3/2*c - [Grünbaumian] ``` ```x3x3o3/2o5/2*a3/2*c - getit dixady x3o3x3/2o5/2*a3/2*c - [Grünbaumian] x3o3o3/2x5/2*a3/2*c - [Grünbaumian] o3x3x3/2o5/2*a3/2*c - (contains "2ike") o3x3o3/2x5/2*a3/2*c - o3o3x3/2x5/2*a3/2*c - [Grünbaumian] x3x3x3/2o5/2*a3/2*c - [Grünbaumian] x3x3o3/2x5/2*a3/2*c - [Grünbaumian] x3o3x3/2x5/2*a3/2*c - [Grünbaumian] o3x3x3/2x5/2*a3/2*c - [Grünbaumian] x3x3x3/2x5/2*a3/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3o3/2o3/2o5/3*a3*c (µ=1063) o3/2o3o3/2o5/3*a3*c (µ=1097) o3/2o3/2o3o5/3*a3/2*c (µ=1663) o3/2o3/2o3/2o5/2*a3/2*c (µ=1937) quasiregulars ```x3o3/2o3/2o5/3*a3*c - (contains "2tet") o3x3/2o3/2o5/3*a3*c - (contains "2tet") o3o3/2x3/2o5/3*a3*c - (contains "2tet") o3o3/2o3/2x5/3*a3*c - gardtaxady ``` ```x3/2o3o3/2o5/3*a3*c - (contains "2tet") o3/2x3o3/2o5/3*a3*c - (contains "2tet") o3/2o3x3/2o5/3*a3*c - (contains "2tet") o3/2o3o3/2x5/3*a3*c - gardtaxady ``` ```x3/2o3/2o3o5/3*a3/2*c - (contains "2tet") o3/2x3/2o3o5/3*a3/2*c - (contains "2tet") o3/2o3/2x3o5/3*a3/2*c - (contains "2tet") o3/2o3/2o3x5/3*a3/2*c - gardtaxady ``` ```x3/2o3/2o3/2o5/2*a3/2*c - (contains "2tet") o3/2x3/2o3/2o5/2*a3/2*c - (contains "2tet") o3/2o3/2x3/2o5/2*a3/2*c - (contains "2tet") o3/2o3/2o3/2x5/2*a3/2*c - gardtaxady ``` otherWythoffians ```x3x3/2o3/2o5/3*a3*c - getit dixady x3o3/2x3/2o5/3*a3*c - sefdit dixdy x3o3/2o3/2x5/3*a3*c - (contains "2tet") o3x3/2x3/2o5/3*a3*c - [Grünbaumian] o3x3/2o3/2x5/3*a3*c - o3o3/2x3/2x5/3*a3*c - [Grünbaumian] x3x3/2x3/2o5/3*a3*c - [Grünbaumian] x3x3/2o3/2x5/3*a3*c - x3o3/2x3/2x5/3*a3*c - [Grünbaumian] o3x3/2x3/2x5/3*a3*c - [Grünbaumian] x3x3/2x3/2x5/3*a3*c - [Grünbaumian] ``` ```x3/2x3o3/2o5/3*a3*c - [Grünbaumian] x3/2o3x3/2o5/3*a3*c - sefdit dixdy x3/2o3o3/2x5/3*a3*c - (contains "2tet") o3/2x3x3/2o5/3*a3*c - (contains "2ike") o3/2x3o3/2x5/3*a3*c - o3/2o3x3/2x5/3*a3*c - [Grünbaumian] x3/2x3x3/2o5/3*a3*c - [Grünbaumian] x3/2x3o3/2x5/3*a3*c - [Grünbaumian] x3/2o3x3/2x5/3*a3*c - [Grünbaumian] o3/2x3x3/2x5/3*a3*c - [Grünbaumian] x3/2x3x3/2x5/3*a3*c - [Grünbaumian] ``` ```x3/2x3/2o3o5/3*a3/2*c - [Grünbaumian] x3/2o3/2x3o5/3*a3/2*c - [Grünbaumian] x3/2o3/2o3x5/3*a3/2*c - (contains "2tet") o3/2x3/2x3o5/3*a3/2*c - [Grünbaumian] o3/2x3/2o3x5/3*a3/2*c - o3/2o3/2x3x5/3*a3/2*c - (contains "2tet") x3/2x3/2x3o5/3*a3/2*c - [Grünbaumian] x3/2x3/2o3x5/3*a3/2*c - [Grünbaumian] x3/2o3/2x3x5/3*a3/2*c - [Grünbaumian] o3/2x3/2x3x5/3*a3/2*c - [Grünbaumian] x3/2x3/2x3x5/3*a3/2*c - [Grünbaumian] ``` ```x3/2x3/2o3/2o5/2*a3/2*c - [Grünbaumian] x3/2o3/2x3/2o5/2*a3/2*c - [Grünbaumian] x3/2o3/2o3/2x5/2*a3/2*c - [Grünbaumian] o3/2x3/2x3/2o5/2*a3/2*c - [Grünbaumian] o3/2x3/2o3/2x5/2*a3/2*c - o3/2o3/2x3/2x5/2*a3/2*c - [Grünbaumian] x3/2x3/2x3/2o5/2*a3/2*c - [Grünbaumian] x3/2x3/2o3/2x5/2*a3/2*c - [Grünbaumian] x3/2o3/2x3/2x5/2*a3/2*c - [Grünbaumian] o3/2x3/2x3/2x5/2*a3/2*c - [Grünbaumian] x3/2x3/2x3/2x5/2*a3/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5/2o5*a3/2*c   (up)

 o3o3o5/2o5*a3/2*c (µ=48) o3o3/2o5/3o5*a3*c (µ=72) o3/2o3o5/3o5*a3*c (µ=408) o3/2o3o5/2o5/4*a3*c (µ=792) quasiregulars ```x3o3o5/2o5*a3/2*c - (contains "2tet") o3x3o5/2o5*a3/2*c - (contains "2tet") o3o3x5/2o5*a3/2*c - (contains "2tet") o3o3o5/2x5*a3/2*c - dattathi ``` ```x3o3/2o5/3o5*a3*c - (contains "2tet") o3x3/2o5/3o5*a3*c - (contains "2tet") o3o3/2x5/3o5*a3*c - (contains "2tet") o3o3/2o5/3x5*a3*c - dattathi ``` ```x3/2o3o5/3o5*a3*c - (contains "2tet") o3/2x3o5/3o5*a3*c - (contains "2tet") o3/2o3x5/3o5*a3*c - (contains "2tet") o3/2o3o5/3x5*a3*c - dattathi ``` ```x3/2o3o5/2o5/4*a3*c - (contains "2tet") o3/2x3o5/2o5/4*a3*c - (contains "2tet") o3/2o3x5/2o5/4*a3*c - (contains "2tet") o3/2o3o5/2x5/4*a3*c - dattathi ``` otherWythoffians ```x3x3o5/2o5*a3/2*c - (contains cid) x3o3x5/2o5*a3/2*c - [Grünbaumian] x3o3o5/2x5*a3/2*c - (contains "2tet") o3x3x5/2o5*a3/2*c - (contains gacid) o3x3o5/2x5*a3/2*c - o3o3x5/2x5*a3/2*c - [Grünbaumian] x3x3x5/2o5*a3/2*c - [Grünbaumian] x3x3o5/2x5*a3/2*c - x3o3x5/2x5*a3/2*c - [Grünbaumian] o3x3x5/2x5*a3/2*c - [Grünbaumian] x3x3x5/2x5*a3/2*c - [Grünbaumian] ``` ```x3x3/2o5/3o5*a3*c - (contains cid) x3o3/2x5/3o5*a3*c - efdit xithi x3o3/2o5/3x5*a3*c - (contains "2tet") o3x3/2x5/3o5*a3*c - [Grünbaumian] o3x3/2o5/3x5*a3*c - o3o3/2x5/3x5*a3*c - (contains "2tet") x3x3/2x5/3o5*a3*c - [Grünbaumian] x3x3/2o5/3x5*a3*c - x3o3/2x5/3x5*a3*c - xhidy o3x3/2x5/3x5*a3*c - [Grünbaumian] x3x3/2x5/3x5*a3*c - [Grünbaumian] ``` ```x3/2x3o5/3o5*a3*c - [Grünbaumian] x3/2o3x5/3o5*a3*c - efdit xithi x3/2o3o5/3x5*a3*c - (contains "2tet") o3/2x3x5/3o5*a3*c - (contains gacid) o3/2x3o5/3x5*a3*c - o3/2o3x5/3x5*a3*c - (contains "2tet") x3/2x3x5/3o5*a3*c - [Grünbaumian] x3/2x3o5/3x5*a3*c - [Grünbaumian] x3/2o3x5/3x5*a3*c - xhidy o3/2x3x5/3x5*a3*c - x3/2x3x5/3x5*a3*c - [Grünbaumian] ``` ```x3/2x3o5/2o5/4*a3*c - [Grünbaumian] x3/2o3x5/2o5/4*a3*c - efdit xithi x3/2o3o5/2x5/4*a3*c - [Grünbaumian] o3/2x3x5/2o5/4*a3*c - (contains gacid) o3/2x3o5/2x5/4*a3*c - o3/2o3x5/2x5/4*a3*c - [Grünbaumian] x3/2x3x5/2o5/4*a3*c - [Grünbaumian] x3/2x3o5/2x5/4*a3*c - [Grünbaumian] x3/2o3x5/2x5/4*a3*c - [Grünbaumian] o3/2x3x5/2x5/4*a3*c - [Grünbaumian] x3/2x3x5/2x5/4*a3*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o3/2o5/2o5*a3/2*c (µ=912) o3o3/2o5/2o5/4*a3*c (µ=1128) o3o3o5/3o5/4*a3/2*c (µ=1152) o3/2o3/2o5/3o5/4*a3/2*c (µ=2688) quasiregulars ```x3/2o3/2o5/2o5*a3/2*c - (contains "2tet") o3/2x3/2o5/2o5*a3/2*c - (contains "2tet") o3/2o3/2x5/2o5*a3/2*c - (contains "2tet") o3/2o3/2o5/2x5*a3/2*c - dattathi ``` ```x3o3/2o5/2o5/4*a3*c - (contains "2tet") o3x3/2o5/2o5/4*a3*c - (contains "2tet") o3o3/2x5/2o5/4*a3*c - (contains "2tet") o3o3/2o5/2x5/4*a3*c - dattathi ``` ```x3o3o5/3o5/4*a3/2*c - (contains "2tet") o3x3o5/3o5/4*a3/2*c - (contains "2tet") o3o3x5/3o5/4*a3/2*c - (contains "2tet") o3o3o5/3x5/4*a3/2*c - dattathi ``` ```x3/2o3/2o5/3o5/4*a3/2*c - (contains "2tet") o3/2x3/2o5/3o5/4*a3/2*c - (contains "2tet") o3/2o3/2x5/3o5/4*a3/2*c - (contains "2tet") o3/2o3/2o5/3x5/4*a3/2*c - dattathi ``` otherWythoffians ```x3/2x3/2o5/2o5*a3/2*c - [Grünbaumian] x3/2o3/2x5/2o5*a3/2*c - [Grünbaumian] x3/2o3/2o5/2x5*a3/2*c - (contains "2tet") o3/2x3/2x5/2o5*a3/2*c - [Grünbaumian] o3/2x3/2o5/2x5*a3/2*c - o3/2o3/2x5/2x5*a3/2*c - [Grünbaumian] x3/2x3/2x5/2o5*a3/2*c - [Grünbaumian] x3/2x3/2o5/2x5*a3/2*c - [Grünbaumian] x3/2o3/2x5/2x5*a3/2*c - [Grünbaumian] o3/2x3/2x5/2x5*a3/2*c - [Grünbaumian] x3/2x3/2x5/2x5*a3/2*c - [Grünbaumian] ``` ```x3x3/2o5/2o5/4*a3*c - (contains cid) x3o3/2x5/2o5/4*a3*c - efdit xithi x3o3/2o5/2x5/4*a3*c - [Grünbaumian] o3x3/2x5/2o5/4*a3*c - [Grünbaumian] o3x3/2o5/2x5/4*a3*c - o3o3/2x5/2x5/4*a3*c - [Grünbaumian] x3x3/2x5/2o5/4*a3*c - [Grünbaumian] x3x3/2o5/2x5/4*a3*c - [Grünbaumian] x3o3/2x5/2x5/4*a3*c - [Grünbaumian] o3x3/2x5/2x5/4*a3*c - [Grünbaumian] x3x3/2x5/2x5/4*a3*c - [Grünbaumian] ``` ```x3x3o5/3o5/4*a3/2*c - (contains cid) x3o3x5/3o5/4*a3/2*c - [Grünbaumian] x3o3o5/3x5/4*a3/2*c - [Grünbaumian] o3x3x5/3o5/4*a3/2*c - (contains gacid) o3x3o5/3x5/4*a3/2*c - o3o3x5/3x5/4*a3/2*c - (contains "2tet") x3x3x5/3o5/4*a3/2*c - [Grünbaumian] x3x3o5/3x5/4*a3/2*c - [Grünbaumian] x3o3x5/3x5/4*a3/2*c - [Grünbaumian] o3x3x5/3x5/4*a3/2*c - x3x3x5/3x5/4*a3/2*c - [Grünbaumian] ``` ```x3/2x3/2o5/3o5/4*a3/2*c - [Grünbaumian] x3/2o3/2x5/3o5/4*a3/2*c - [Grünbaumian] x3/2o3/2o5/3x5/4*a3/2*c - [Grünbaumian] o3/2x3/2x5/3o5/4*a3/2*c - [Grünbaumian] o3/2x3/2o5/3x5/4*a3/2*c - o3/2o3/2x5/3x5/4*a3/2*c - (contains "2tet") x3/2x3/2x5/3o5/4*a3/2*c - [Grünbaumian] x3/2x3/2o5/3x5/4*a3/2*c - [Grünbaumian] x3/2o3/2x5/3x5/4*a3/2*c - [Grünbaumian] o3/2x3/2x5/3x5/4*a3/2*c - [Grünbaumian] x3/2x3/2x5/3x5/4*a3/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5/2o5o3/2*a3*c   (up)

 o3o5/2o5o3/2*a3*c (µ=35) o3o5/2o5/4o3*a3*c (µ=205) o3/2o5/2o5o3*a3/2*c (µ=325) o3o5/3o5o3*a3/2*c (µ=395) quasiregulars ```x3o5/2o5o3/2*a3*c - (contains "2ike") o3x5/2o5o3/2*a3*c - sishi+gridixhi (?) o3o5/2x5o3/2*a3*c - datcathi o3o5/2o5x3/2*a3*c - gaghi+sridixhi (?) ``` ```x3o5/2o5/4o3*a3*c - (contains "2ike") o3x5/2o5/4o3*a3*c - sishi+gridixhi (?) o3o5/2x5/4o3*a3*c - datcathi o3o5/2o5/4x3*a3*c - gaghi+sridixhi (?) ``` ```x3/2o5/2o5o3*a3/2*c - (contains "2ike") o3/2x5/2o5o3*a3/2*c - sishi+gridixhi (?) o3/2o5/2x5o3*a3/2*c - datcathi o3/2o5/2o5x3*a3/2*c - gaghi+sridixhi (?) ``` ```x3o5/3o5o3*a3/2*c - (contains "2ike") o3x5/3o5o3*a3/2*c - sishi+gridixhi (?) o3o5/3x5o3*a3/2*c - datcathi o3o5/3o5x3*a3/2*c - gaghi+sridixhi (?) ``` otherWythoffians ```x3x5/2o5o3/2*a3*c - (contains "2gike") x3o5/2x5o3/2*a3*c - girfixthi x3o5/2o5x3/2*a3*c - [Grünbaumian] o3x5/2x5o3/2*a3*c - [Grünbaumian] o3x5/2o5x3/2*a3*c - o3o5/2x5x3/2*a3*c - (contains "2seihid") x3x5/2x5o3/2*a3*c - [Grünbaumian] x3x5/2o5x3/2*a3*c - [Grünbaumian] x3o5/2x5x3/2*a3*c - [Grünbaumian] o3x5/2x5x3/2*a3*c - [Grünbaumian] x3x5/2x5x3/2*a3*c - [Grünbaumian] ``` ```x3x5/2o5/4o3*a3*c - (contains "2gike") x3o5/2x5/4o3*a3*c - girfixthi x3o5/2o5/4x3*a3*c - (contains "2ike") o3x5/2x5/4o3*a3*c - [Grünbaumian] o3x5/2o5/4x3*a3*c - o3o5/2x5/4x3*a3*c - [Grünbaumian] x3x5/2x5/4o3*a3*c - [Grünbaumian] x3x5/2o5/4x3*a3*c - x3o5/2x5/4x3*a3*c - [Grünbaumian] o3x5/2x5/4x3*a3*c - [Grünbaumian] x3x5/2x5/4x3*a3*c - [Grünbaumian] ``` ```x3/2x5/2o5o3*a3/2*c - [Grünbaumian] x3/2o5/2x5o3*a3/2*c - [Grünbaumian] x3/2o5/2o5x3*a3/2*c - (contains "2ike") o3/2x5/2x5o3*a3/2*c - [Grünbaumian] o3/2x5/2o5x3*a3/2*c - o3/2o5/2x5x3*a3/2*c - (contains "2seihid") x3/2x5/2x5o3*a3/2*c - [Grünbaumian] x3/2x5/2o5x3*a3/2*c - [Grünbaumian] x3/2o5/2x5x3*a3/2*c - [Grünbaumian] o3/2x5/2x5x3*a3/2*c - [Grünbaumian] x3/2x5/2x5x3*a3/2*c - [Grünbaumian] ``` ```x3x5/3o5o3*a3/2*c - (contains "2gike") x3o5/3x5o3*a3/2*c - [Grünbaumian] x3o5/3o5x3*a3/2*c - (contains "2ike") o3x5/3x5o3*a3/2*c - (contains "2geihid") o3x5/3o5x3*a3/2*c - o3o5/3x5x3*a3/2*c - (contains "2seihid") x3x5/3x5o3*a3/2*c - [Grünbaumian] x3x5/3o5x3*a3/2*c - x3o5/3x5x3*a3/2*c - [Grünbaumian] o3x5/3x5x3*a3/2*c - x3x5/3x5x3*a3/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o5/3o5o3/2*a3*c (µ=685) o3/2o5/3o5/4o3*a3*c (µ=1475) o3o5/3o5/4o3/2*a3/2*c (µ=1765) o3/2o5/2o5/4o3/2*a3/2*c (µ=2315) quasiregulars ```x3/2o5/3o5o3/2*a3*c - (contains "2ike") o3/2x5/3o5o3/2*a3*c - sishi+gridixhi (?) o3/2o5/3x5o3/2*a3*c - datcathi o3/2o5/3o5x3/2*a3*c - gaghi+sridixhi (?) ``` ```x3/2o5/3o5/4o3*a3*c - (contains "2ike") o3/2x5/3o5/4o3*a3*c - sishi+gridixhi (?) o3/2o5/3x5/4o3*a3*c - datcathi o3/2o5/3o5/4x3*a3*c - gaghi+sridixhi (?) ``` ```x3o5/3o5/4o3/2*a3/2*c - (contains "2ike") o3x5/3o5/4o3/2*a3/2*c - sishi+gridixhi (?) o3o5/3x5/4o3/2*a3/2*c - datcathi o3o5/3o5/4x3/2*a3/2*c - gaghi+sridixhi (?) ``` ```x3/2o5/2o5/4o3/2*a3/2*c - (contains "2ike") o3/2x5/2o5/4o3/2*a3/2*c - sishi+gridixhi (?) o3/2o5/2x5/4o3/2*a3/2*c - datcathi o3/2o5/2o5/4x3/2*a3/2*c - gaghi+sridixhi (?) ``` otherWythoffians ```x3/2x5/3o5o3/2*a3*c - [Grünbaumian] x3/2o5/3x5o3/2*a3*c - girfixthi x3/2o5/3o5x3/2*a3*c - [Grünbaumian] o3/2x5/3x5o3/2*a3*c - (contains "2geihid") o3/2x5/3o5x3/2*a3*c - o3/2o5/3x5x3/2*a3*c - (contains "2seihid") x3/2x5/3x5o3/2*a3*c - [Grünbaumian] x3/2x5/3o5x3/2*a3*c - [Grünbaumian] x3/2o5/3x5x3/2*a3*c - [Grünbaumian] o3/2x5/3x5x3/2*a3*c - x3/2x5/3x5x3/2*a3*c - [Grünbaumian] ``` ```x3/2x5/3o5/4o3*a3*c - [Grünbaumian] x3/2o5/3x5/4o3*a3*c - girfixthi x3/2o5/3o5/4x3*a3*c - (contains "2ike") o3/2x5/3x5/4o3*a3*c - (contains "2geihid") o3/2x5/3o5/4x3*a3*c - o3/2o5/3x5/4x3*a3*c - [Grünbaumian] x3/2x5/3x5/4o3*a3*c - [Grünbaumian] x3/2x5/3o5/4x3*a3*c - [Grünbaumian] x3/2o5/3x5/4x3*a3*c - [Grünbaumian] o3/2x5/3x5/4x3*a3*c - [Grünbaumian] x3/2x5/3x5/4x3*a3*c - [Grünbaumian] ``` ```x3x5/3o5/4o3/2*a3/2*c - (contains "2gike") x3o5/3x5/4o3/2*a3/2*c - [Grünbaumian] x3o5/3o5/4x3/2*a3/2*c - [Grünbaumian] o3x5/3x5/4o3/2*a3/2*c - (contains "2geihid") o3x5/3o5/4x3/2*a3/2*c - o3o5/3x5/4x3/2*a3/2*c - [Grünbaumian] x3x5/3x5/4o3/2*a3/2*c - [Grünbaumian] x3x5/3o5/4x3/2*a3/2*c - [Grünbaumian] x3o5/3x5/4x3/2*a3/2*c - [Grünbaumian] o3x5/3x5/4x3/2*a3/2*c - [Grünbaumian] x3x5/3x5/4x3/2*a3/2*c - [Grünbaumian] ``` ```x3/2x5/2o5/4o3/2*a3/2*c - [Grünbaumian] x3/2o5/2x5/4o3/2*a3/2*c - [Grünbaumian] x3/2o5/2o5/4x3/2*a3/2*c - [Grünbaumian] o3/2x5/2x5/4o3/2*a3/2*c - [Grünbaumian] o3/2x5/2o5/4x3/2*a3/2*c - o3/2o5/2x5/4x3/2*a3/2*c - [Grünbaumian] x3/2x5/2x5/4o3/2*a3/2*c - [Grünbaumian] x3/2x5/2o5/4x3/2*a3/2*c - [Grünbaumian] x3/2o5/2x5/4x3/2*a3/2*c - [Grünbaumian] o3/2x5/2x5/4x3/2*a3/2*c - [Grünbaumian] x3/2x5/2x5/4x3/2*a3/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5o5/2o5/2*a3/2*c   (up)

 o3o5o5/2o5/2*a3/2*c (µ=126) o3/2o5o5/2o5/3*a3*c (µ=234) o3/2o5o5/3o5/2*a3*c (µ=486) o3o5o5/3o5/3*a3/2*c (µ=594) quasiregulars ```x3o5o5/2o5/2*a3/2*c - (contains gacid) o3x5o5/2o5/2*a3/2*c - gaghi+didhi (?) o3o5x5/2o5/2*a3/2*c - (contains gacid) o3o5o5/2x5/2*a3/2*c - (contains "2gissid") ``` ```x3/2o5o5/2o5/3*a3*c - (contains gacid) o3/2x5o5/2o5/3*a3*c - gaghi+didhi (?) o3/2o5x5/2o5/3*a3*c - (contains gacid) o3/2o5o5/2x5/3*a3*c - (contains "2gissid") ``` ```x3/2o5o5/3o5/2*a3*c - (contains gacid) o3/2x5o5/3o5/2*a3*c - gaghi+didhi (?) o3/2o5x5/3o5/2*a3*c - (contains gacid) o3/2o5o5/3x5/2*a3*c - (contains "2gissid") ``` ```x3o5o5/3o5/3*a3/2*c - (contains gacid) o3x5o5/3o5/3*a3/2*c - gaghi+didhi (?) o3o5x5/3o5/3*a3/2*c - (contains gacid) o3o5o5/3x5/3*a3/2*c - (contains "2gissid") ``` otherWythoffians ```x3x5o5/2o5/2*a3/2*c - (contains gacid) x3o5x5/2o5/2*a3/2*c - [Grünbaumian] x3o5o5/2x5/2*a3/2*c - [Grünbaumian] o3x5x5/2o5/2*a3/2*c - (contains gacid) o3x5o5/2x5/2*a3/2*c - o3o5x5/2x5/2*a3/2*c - [Grünbaumian] x3x5x5/2o5/2*a3/2*c - [Grünbaumian] x3x5o5/2x5/2*a3/2*c - [Grünbaumian] x3o5x5/2x5/2*a3/2*c - [Grünbaumian] o3x5x5/2x5/2*a3/2*c - [Grünbaumian] x3x5x5/2x5/2*a3/2*c - [Grünbaumian] ``` ```x3/2x5o5/2o5/3*a3*c - [Grünbaumian] x3/2o5x5/2o5/3*a3*c - (contains "2sidhei") x3/2o5o5/2x5/3*a3*c - (contains "2gike") o3/2x5x5/2o5/3*a3*c - (contains gacid) o3/2x5o5/2x5/3*a3*c - o3/2o5x5/2x5/3*a3*c - [Grünbaumian] x3/2x5x5/2o5/3*a3*c - [Grünbaumian] x3/2x5o5/2x5/3*a3*c - [Grünbaumian] x3/2o5x5/2x5/3*a3*c - [Grünbaumian] o3/2x5x5/2x5/3*a3*c - [Grünbaumian] x3/2x5x5/2x5/3*a3*c - [Grünbaumian] ``` ```x3/2x5o5/3o5/2*a3*c - [Grünbaumian] x3/2o5x5/3o5/2*a3*c - (contains "2sidhei") x3/2o5o5/3x5/2*a3*c - [Grünbaumian] o3/2x5x5/3o5/2*a3*c - (contains gacid) o3/2x5o5/3x5/2*a3*c - o3/2o5x5/3x5/2*a3*c - gefidtethi x3/2x5x5/3o5/2*a3*c - [Grünbaumian] x3/2x5o5/3x5/2*a3*c - [Grünbaumian] x3/2o5x5/3x5/2*a3*c - [Grünbaumian] o3/2x5x5/3x5/2*a3*c - x3/2x5x5/3x5/2*a3*c - [Grünbaumian] ``` ```x3x5o5/3o5/3*a3/2*c - (contains gacid) x3o5x5/3o5/3*a3/2*c - [Grünbaumian] x3o5o5/3x5/3*a3/2*c - (contains "2gike") o3x5x5/3o5/3*a3/2*c - (contains gacid) o3x5o5/3x5/3*a3/2*c - o3o5x5/3x5/3*a3/2*c - gefidtethi x3x5x5/3o5/3*a3/2*c - [Grünbaumian] x3x5o5/3x5/3*a3/2*c - x3o5x5/3x5/3*a3/2*c - [Grünbaumian] o3x5x5/3x5/3*a3/2*c - x3x5x5/3x5/3*a3/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3o5/4o5/3o5/2*a3*c (µ=714) o3o5/4o5/2o5/3*a3*c (µ=966) o3/2o5/4o5/2o5/2*a3/2*c (µ=1554) o3/2o5/4o5/3o5/3*a3/2*c (µ=2526) quasiregulars ```x3o5/4o5/3o5/2*a3*c - (contains gacid) o3x5/4o5/3o5/2*a3*c - gaghi+didhi (?) o3o5/4x5/3o5/2*a3*c - (contains gacid) o3o5/4o5/3x5/2*a3*c - (contains "2gissid") ``` ```x3o5/4o5/2o5/3*a3*c - (contains gacid) o3x5/4o5/2o5/3*a3*c - gaghi+didhi (?) o3o5/4x5/2o5/3*a3*c - (contains gacid) o3o5/4o5/2x5/3*a3*c - (contains "2gissid") ``` ```x3/2o5/4o5/2o5/2*a3/2*c - (contains gacid) o3/2x5/4o5/2o5/2*a3/2*c - gaghi+didhi (?) o3/2o5/4x5/2o5/2*a3/2*c - (contains gacid) o3/2o5/4o5/2x5/2*a3/2*c - (contains "2gissid") ``` ```x3/2o5/4o5/3o5/3*a3/2*c - (contains gacid) o3/2x5/4o5/3o5/3*a3/2*c - gaghi+didhi (?) o3/2o5/4x5/3o5/3*a3/2*c - (contains gacid) o3/2o5/4o5/3x5/3*a3/2*c - (contains "2gissid") ``` otherWythoffians ```x3x5/4o5/3o5/2*a3*c - (contains gacid) x3o5/4x5/3o5/2*a3*c - (contains "2sidhei") x3o5/4o5/3x5/2*a3*c - [Grünbaumian] o3x5/4x5/3o5/2*a3*c - [Grünbaumian] o3x5/4o5/3x5/2*a3*c - o3o5/4x5/3x5/2*a3*c - gefidtethi x3x5/4x5/3o5/2*a3*c - [Grünbaumian] x3x5/4o5/3x5/2*a3*c - [Grünbaumian] x3o5/4x5/3x5/2*a3*c - [Grünbaumian] o3x5/4x5/3x5/2*a3*c - [Grünbaumian] x3x5/4x5/3x5/2*a3*c - [Grünbaumian] ``` ```x3x5/4o5/2o5/3*a3*c - (contains gacid) x3o5/4x5/2o5/3*a3*c - (contains "2sidhei") x3o5/4o5/2x5/3*a3*c - (contains "2gike") o3x5/4x5/2o5/3*a3*c - [Grünbaumian] o3x5/4o5/2x5/3*a3*c - o3o5/4x5/2x5/3*a3*c - [Grünbaumian] x3x5/4x5/2o5/3*a3*c - [Grünbaumian] x3x5/4o5/2x5/3*a3*c - x3o5/4x5/2x5/3*a3*c - [Grünbaumian] o3x5/4x5/2x5/3*a3*c - [Grünbaumian] x3x5/4x5/2x5/3*a3*c - [Grünbaumian] ``` ```x3/2x5/4o5/2o5/2*a3/2*c - [Grünbaumian] x3/2o5/4x5/2o5/2*a3/2*c - [Grünbaumian] x3/2o5/4o5/2x5/2*a3/2*c - [Grünbaumian] o3/2x5/4x5/2o5/2*a3/2*c - [Grünbaumian] o3/2x5/4o5/2x5/2*a3/2*c - o3/2o5/4x5/2x5/2*a3/2*c - [Grünbaumian] x3/2x5/4x5/2o5/2*a3/2*c - [Grünbaumian] x3/2x5/4o5/2x5/2*a3/2*c - [Grünbaumian] x3/2o5/4x5/2x5/2*a3/2*c - [Grünbaumian] o3/2x5/4x5/2x5/2*a3/2*c - [Grünbaumian] x3/2x5/4x5/2x5/2*a3/2*c - [Grünbaumian] ``` ```x3/2x5/4o5/3o5/3*a3/2*c - [Grünbaumian] x3/2o5/4x5/3o5/3*a3/2*c - [Grünbaumian] x3/2o5/4o5/3x5/3*a3/2*c - (contains "2gike") o3/2x5/4x5/3o5/3*a3/2*c - [Grünbaumian] o3/2x5/4o5/3x5/3*a3/2*c - o3/2o5/4x5/3x5/3*a3/2*c - gefidtethi x3/2x5/4x5/3o5/3*a3/2*c - [Grünbaumian] x3/2x5/4o5/3x5/3*a3/2*c - [Grünbaumian] x3/2o5/4x5/3x5/3*a3/2*c - [Grünbaumian] o3/2x5/4x5/3x5/3*a3/2*c - [Grünbaumian] x3/2x5/4x5/3x5/3*a3/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5/3o5o5*a3/2*c   (up)

 o3o5/3o5o5*a3/2*c (µ=54) o3o5/2o5/4o5*a3*c (µ=66) o3o5/2o5o5/4*a3*c (µ=174) o3/2o5/2o5o5*a3/2*c (µ=186) quasiregulars ```x3o5/3o5o5*a3/2*c - (contains cid) o3x5/3o5o5*a3/2*c - sishi+ofiddady (?) o3o5/3x5o5*a3/2*c - (contains cid) o3o5/3o5x5*a3/2*c - (contains "2doe") ``` ```x3o5/2o5/4o5*a3*c - (contains cid) o3x5/2o5/4o5*a3*c - sishi+ofiddady (?) o3o5/2x5/4o5*a3*c - (contains cid) o3o5/2o5/4x5*a3*c - (contains "2doe") ``` ```x3o5/2o5o5/4*a3*c - (contains cid) o3x5/2o5o5/4*a3*c - sishi+ofiddady (?) o3o5/2x5o5/4*a3*c - (contains cid) o3o5/2o5x5/4*a3*c - (contains "2doe") ``` ```x3/2o5/2o5o5*a3/2*c - (contains cid) o3/2x5/2o5o5*a3/2*c - sishi+ofiddady (?) o3/2o5/2x5o5*a3/2*c - (contains cid) o3/2o5/2o5x5*a3/2*c - (contains "2doe") ``` otherWythoffians ```x3x5/3o5o5*a3/2*c - (contains cid) x3o5/3x5o5*a3/2*c - [Grünbaumian] x3o5/3o5x5*a3/2*c - (contains "2ike") o3x5/3x5o5*a3/2*c - (contains cid) o3x5/3o5x5*a3/2*c - o3o5/3x5x5*a3/2*c - sefidtethi x3x5/3x5o5*a3/2*c - [Grünbaumian] x3x5/3o5x5*a3/2*c - x3o5/3x5x5*a3/2*c - [Grünbaumian] o3x5/3x5x5*a3/2*c - x3x5/3x5x5*a3/2*c - [Grünbaumian] ``` ```x3x5/2o5/4o5*a3*c - (contains cid) x3o5/2x5/4o5*a3*c - (contains "2gidhei") x3o5/2o5/4x5*a3*c - (contains "2ike") o3x5/2x5/4o5*a3*c - [Grünbaumian] o3x5/2o5/4x5*a3*c - o3o5/2x5/4x5*a3*c - [Grünbaumian] x3x5/2x5/4o5*a3*c - [Grünbaumian] x3x5/2o5/4x5*a3*c - x3o5/2x5/4x5*a3*c - [Grünbaumian] o3x5/2x5/4x5*a3*c - [Grünbaumian] x3x5/2x5/4x5*a3*c - [Grünbaumian] ``` ```x3x5/2o5o5/4*a3*c - (contains cid) x3o5/2x5o5/4*a3*c - (contains "2gidhei") x3o5/2o5x5/4*a3*c - [Grünbaumian] o3x5/2x5o5/4*a3*c - [Grünbaumian] o3x5/2o5x5/4*a3*c - o3o5/2x5x5/4*a3*c - sefidtethi x3x5/2x5o5/4*a3*c - [Grünbaumian] x3x5/2o5x5/4*a3*c - [Grünbaumian] x3o5/2x5x5/4*a3*c - [Grünbaumian] o3x5/2x5x5/4*a3*c - [Grünbaumian] x3x5/2x5x5/4*a3*c - [Grünbaumian] ``` ```x3/2x5/2o5o5*a3/2*c - [Grünbaumian] x3/2o5/2x5o5*a3/2*c - [Grünbaumian] x3/2o5/2o5x5*a3/2*c - (contains "2ike") o3/2x5/2x5o5*a3/2*c - [Grünbaumian] o3/2x5/2o5x5*a3/2*c - o3/2o5/2x5x5*a3/2*c - sefidtethi x3/2x5/2x5o5*a3/2*c - [Grünbaumian] x3/2x5/2o5x5*a3/2*c - [Grünbaumian] x3/2o5/2x5x5*a3/2*c - [Grünbaumian] o3/2x5/2x5x5*a3/2*c - [Grünbaumian] x3/2x5/2x5x5*a3/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o5/3o5o5/4*a3*c (µ=1026) o3/2o5/3o5/4o5*a3*c (µ=1134) o3o5/3o5/4o5/4*a3/2*c (µ=2106) o3/2o5/2o5/4o5/4*a3/2*c (µ=2454) quasiregulars ```x3/2o5/3o5o5/4*a3*c - (contains cid) o3/2x5/3o5o5/4*a3*c - sishi+ofiddady (?) o3/2o5/3x5o5/4*a3*c - (contains cid) o3/2o5/3o5x5/4*a3*c - (contains "2doe") ``` ```x3/2o5/3o5/4o5*a3*c - (contains cid) o3/2x5/3o5/4o5*a3*c - sishi+ofiddady (?) o3/2o5/3x5/4o5*a3*c - (contains cid) o3/2o5/3o5/4x5*a3*c - (contains "2doe") ``` ```x3/2o5/3o5/4o5/4*a3/2*c - (contains cid) o3x5/3o5/4o5/4*a3/2*c - sishi+ofiddady (?) o3o5/3x5/4o5/4*a3/2*c - (contains cid) o3o5/3o5/4x5/4*a3/2*c - (contains "2doe") ``` ```x3/2o5/2o5/4o5/4*a3/2*c - (contains cid) o3/2x5/2o5/4o5/4*a3/2*c - sishi+ofiddady (?) o3/2o5/2x5/4o5/4*a3/2*c - (contains cid) o3/2o5/2o5/4x5/4*a3/2*c - (contains "2doe") ``` otherWythoffians ```x3/2x5/3o5o5/4*a3*c - [Grünbaumian] x3/2o5/3x5o5/4*a3*c - (contains "2gidhei") x3/2o5/3o5x5/4*a3*c - [Grünbaumian] o3/2x5/3x5o5/4*a3*c - (contains cid) o3/2x5/3o5x5/4*a3*c - o3/2o5/3x5x5/4*a3*c - sefidtethi x3/2x5/3x5o5/4*a3*c - [Grünbaumian] x3/2x5/3o5x5/4*a3*c - [Grünbaumian] x3/2o5/3x5x5/4*a3*c - [Grünbaumian] o3/2x5/3x5x5/4*a3*c - x3/2x5/3x5x5/4*a3*c - [Grünbaumian] ``` ```x3/2x5/3o5/4o5*a3*c - [Grünbaumian] x3/2o5/3x5/4o5*a3*c - (contains "2gidhei") x3/2o5/3o5/4x5*a3*c - (contains "2ike") o3/2x5/3x5/4o5*a3*c - (contains cid) o3/2x5/3o5/4x5*a3*c - o3/2o5/3x5/4x5*a3*c - [Grünbaumian] x3/2x5/3x5/4o5*a3*c - [Grünbaumian] x3/2x5/3o5/4x5*a3*c - [Grünbaumian] x3/2o5/3x5/4x5*a3*c - [Grünbaumian] o3/2x5/3x5/4x5*a3*c - [Grünbaumian] x3/2x5/3x5/4x5*a3*c - [Grünbaumian] ``` ```x3x5/3o5/4o5/4*a3/2*c - (contains cid) x3o5/3x5/4o5/4*a3/2*c - [Grünbaumian] x3o5/3o5/4x5/4*a3/2*c - [Grünbaumian] o3x5/3x5/4o5/4*a3/2*c - (contains cid) o3x5/3o5/4x5/4*a3/2*c - o3o5/3x5/4x5/4*a3/2*c - [Grünbaumian] x3x5/3x5/4o5/4*a3/2*c - [Grünbaumian] x3x5/3o5/4x5/4*a3/2*c - [Grünbaumian] x3o5/3x5/4x5/4*a3/2*c - [Grünbaumian] o3x5/3x5/4x5/4*a3/2*c - [Grünbaumian] x3x5/3x5/4x5/4*a3/2*c - [Grünbaumian] ``` ```x3/2x5/2o5/4o5/4*a3/2*c - [Grünbaumian] x3/2o5/2x5/4o5/4*a3/2*c - [Grünbaumian] x3/2o5/2o5/4x5/4*a3/2*c - [Grünbaumian] o3/2x5/2x5/4o5/4*a3/2*c - [Grünbaumian] o3/2x5/2o5/4x5/4*a3/2*c - o3/2o5/2x5/4x5/4*a3/2*c - [Grünbaumian] x3/2x5/2x5/4o5/4*a3/2*c - [Grünbaumian] x3/2x5/2o5/4x5/4*a3/2*c - [Grünbaumian] x3/2o5/2x5/4x5/4*a3/2*c - [Grünbaumian] o3/2x5/2x5/4x5/4*a3/2*c - [Grünbaumian] x3/2x5/2x5/4x5/4*a3/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5o5/2o5o5/2*a3/2*c   (up)

 o5o5/2o5o5/2*a3/2*c (µ=70) o5o5/3o5o5/3*a3*c (µ=190) o5o5/3o5/4o5/2*a3*c (µ=290) quasiregulars ```x5o5/2o5o5/2*a3/2*c - (contains cid) o5x5/2o5o5/2*a3/2*c - sishi+gaghi+idhi (?) ``` ```x5o5/3o5o5/3*a3*c - (contains cid) o5x5/3o5o5/3*a3*c - sishi+gaghi+idhi (?) ``` ```x5o5/3o5/4o5/2*a3*c - (contains cid) o5x5/3o5/4o5/2*a3*c - sishi+gaghi+idhi (?) o5o5/3x5/4o5/2*a3*c - (contains cid) o5o5/3o5/4x5/2*a3*c - sishi+gaghi+idhi (?) ``` otherWythoffians ```x5x5/2o5o5/2*a3/2*c - (contains gacid) x5o5/2x5o5/2*a3/2*c - [Grünbaumian] x5o5/2o5x5/2*a3/2*c - [Grünbaumian] o5x5/2o5x5/2*a3/2*c - x5x5/2x5o5/2*a3/2*c - [Grünbaumian] x5x5/2o5x5/2*a3/2*c - [Grünbaumian] x5x5/2x5x5/2*a3/2*c - [Grünbaumian] ``` ```x5x5/3o5o5/3*a3*c - (contains gacid) x5o5/3x5o5/3*a3*c - "2dittafady" x5o5/3o5x5/3*a3*c - (contains cid) o5x5/3o5x5/3*a3*c - x5x5/3x5o5/3*a3*c - ebdah hithi x5x5/3o5x5/3*a3*c - x5x5/3x5x5/3*a3*c - ``` ```x5x5/3o5/4o5/2*a3*c - (contains gacid) x5o5/3x5/4o5/2*a3*c - "2dittafady" x5o5/3o5/4x5/2*a3*c - [Grünbaumian] o5x5/3x5/4o5/2*a3*c - o5x5/3o5/4x5/2*a3*c - o5o5/3x5/4x5/2*a3*c - [Grünbaumian] x5x5/3x5/4o5/2*a3*c - ebdah hithi x5x5/3o5/4x5/2*a3*c - [Grünbaumian] x5o5/3x5/4x5/2*a3*c - [Grünbaumian] o5x5/3x5/4x5/2*a3*c - [Grünbaumian] x5x5/3x5/4x5/2*a3*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5o5/2o5/4o5/3*a3/2*c (µ=890) o5/4o5/2o5/4o5/2*a3*c (µ=1630) o5/4o5/3o5/4o5/3*a3/2*c (µ=2950) quasiregulars ```x5o5/2o5/4o5/3*a3/2*c - (contains cid) o5x5/2o5/4o5/3*a3/2*c - sishi+gaghi+idhi (?) o5o5/2x5/4o5/3*a3/2*c - (contains cid) o5o5/2o5/4x5/3*a3/2*c - sishi+gaghi+idhi (?) ``` ```x5/4o5/2o5/4o5/2*a3*c - (contains cid) o5/4x5/2o5/4o5/2*a3*c - sishi+gaghi+idhi (?) ``` ```x5/4o5/3o5/4o5/3*a3/2*c - (contains cid) o5/4x5/3o5/4o5/3*a3/2*c - sishi+gaghi+idhi (?) ``` otherWythoffians ```x5x5/2o5/4o5/3*a3/2*c - (contains gacid) x5o5/2x5/4o5/3*a3/2*c - [Grünbaumian] x5o5/2o5/4x5/3*a3/2*c - (contains cid) o5x5/2x5/4o5/3*a3/2*c - [Grünbaumian] o5x5/2o5/4x5/3*a3/2*c - o5o5/2x5/4x5/3*a3/2*c - [Grünbaumian] x5x5/2x5/4o5/3*a3/2*c - [Grünbaumian] x5x5/2o5/4x5/3*a3/2*c - x5o5/2x5/4x5/3*a3/2*c - [Grünbaumian] o5x5/2x5/4x5/3*a3/2*c - [Grünbaumian] x5x5/2x5/4x5/3*a3/2*c - [Grünbaumian] ``` ```x5/4x5/2o5/4o5/2*a3*c - [Grünbaumian] x5/4o5/2x5/4o5/2*a3*c - "2dittafady" x5/4o5/2o5/4x5/2*a3*c - [Grünbaumian] o5/4x5/2o5/4x5/2*a3*c - x5/4x5/2x5/4o5/2*a3*c - [Grünbaumian] x5/4x5/2o5/4x5/2*a3*c - [Grünbaumian] x5/4x5/2x5/4x5/2*a3*c - [Grünbaumian] ``` ```x5/4x5/3o5/4o5/3*a3/2*c - [Grünbaumian] x5/4o5/3x5/4o5/3*a3/2*c - [Grünbaumian] x5/4o5/3o5/4x5/3*a3/2*c - (contains cid) o5/4x5/3o5/4x5/3*a3/2*c - x5/4x5/3x5/4o5/3*a3/2*c - [Grünbaumian] x5/4x5/3o5/4x5/3*a3/2*c - [Grünbaumian] x5/4x5/3x5/4x5/3*a3/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3/2o3/2o5*a5*c   (up)

 o3o3/2o3/2o5*a5*c (µ=21) o3o3o3o5*a5/4*c (µ=99) o3/2o3o3/2o5*a5*c (µ=219) o3/2o3o3o5/4*a5*c (µ=501) quasiregulars ```x3o3/2o3/2o5*a5*c - (contains "2doe") o3x3/2o3/2o5*a5*c - (contains "2gike") o3o3/2x3/2o5*a5*c - (contains cid) o3o3/2o3/2x5*a5*c - (contains cid) ``` ```x3o3o3o5*a5/4*c - (contains "2doe") o3x3o3o5*a5/4*c - (contains "2gike") o3o3x3o5*a5/4*c - (contains cid) o3o3o3x5*a5/4*c - (contains cid) ``` ```x3/2o3o3/2o5*a5*c - (contains "2doe") o3/2x3o3/2o5*a5*c - (contains "2gike") o3/2o3x3/2o5*a5*c - (contains cid) o3/2o3o3/2x5*a5*c - (contains cid) ``` ```x3/2o3o3o5/4*a5*c - (contains "2doe") o3/2x3o3o5/4*a5*c - (contains "2gike") o3/2o3x3o5/4*a5*c - (contains cid) o3/2o3o3x5/4*a5*c - (contains cid) ``` otherWythoffians ```x3x3/2o3/2o5*a5*c - (contains "2doe") x3o3/2x3/2o5*a5*c - (contains "2seihid") x3o3/2o3/2x5*a5*c - stut xethi o3x3/2x3/2o5*a5*c - [Grünbaumian] o3x3/2o3/2x5*a5*c - o3o3/2x3/2x5*a5*c - [Grünbaumian] x3x3/2x3/2o5*a5*c - [Grünbaumian] x3x3/2o3/2x5*a5*c - sik vixathi x3o3/2x3/2x5*a5*c - [Grünbaumian] o3x3/2x3/2x5*a5*c - [Grünbaumian] x3x3/2x3/2x5*a5*c - [Grünbaumian] ``` ```x3x3o3o5*a5/4*c - (contains "2doe") x3o3x3o5*a5/4*c - [Grünbaumian] x3o3o3x5*a5/4*c - stut xethi o3x3x3o5*a5/4*c - (contains cid) o3x3o3x5*a5/4*c - o3o3x3x5*a5/4*c - (contains "2gidhei") x3x3x3o5*a5/4*c - [Grünbaumian] x3x3o3x5*a5/4*c - sik vixathi x3o3x3x5*a5/4*c - [Grünbaumian] o3x3x3x5*a5/4*c - x3x3x3x5*a5/4*c - [Grünbaumian] ``` ```x3/2x3o3/2o5*a5*c - [Grünbaumian] x3/2o3x3/2o5*a5*c - (contains "2seihid") x3/2o3o3/2x5*a5*c - stut xethi o3/2x3x3/2o5*a5*c - (contains cid) o3/2x3o3/2x5*a5*c - o3/2o3x3/2x5*a5*c - [Grünbaumian] x3/2x3x3/2o5*a5*c - [Grünbaumian] x3/2x3o3/2x5*a5*c - [Grünbaumian] x3/2o3x3/2x5*a5*c - [Grünbaumian] o3/2x3x3/2x5*a5*c - [Grünbaumian] x3/2x3x3/2x5*a5*c - [Grünbaumian] ``` ```x3/2x3o3o5/4*a5*c - [Grünbaumian] x3/2o3x3o5/4*a5*c - (contains "2seihid") x3/2o3o3x5/4*a5*c - [Grünbaumian] o3/2x3x3o5/4*a5*c - (contains cid) o3/2x3o3x5/4*a5*c - o3/2o3x3x5/4*a5*c - (contains "2gidhei") x3/2x3x3o5/4*a5*c - [Grünbaumian] x3/2x3o3x5/4*a5*c - [Grünbaumian] x3/2o3x3x5/4*a5*c - [Grünbaumian] o3/2x3x3x5/4*a5*c - x3/2x3x3x5/4*a5*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3o3/2o3o5/4*a5*c (µ=699) o3/2o3/2o3o5*a5/4*c (µ=1101) o3o3o3/2o5/4*a5/4*c (µ=1581) o3/2o3/2o3/2o5/4*a5/4*c (µ=2979) quasiregulars ```x3o3/2o3o5/4*a5*c - (contains "2doe") o3x3/2o3o5/4*a5*c - (contains "2gike") o3o3/2x3o5/4*a5*c - (contains cid) o3o3/2o3x5/4*a5*c - (contains cid) ``` ```x3/2o3/2o3o5*a5/4*c - (contains "2doe") o3/2x3/2o3o5*a5/4*c - (contains "2gike") o3/2o3/2x3o5*a5/4*c - (contains cid) o3/2o3/2o3x5*a5/4*c - (contains cid) ``` ```x3o3o3/2o5/4*a5/4*c - (contains "2doe") o3x3o3/2o5/4*a5/4*c - (contains "2gike") o3o3x3/2o5/4*a5/4*c - (contains cid) o3o3o3/2x5/4*a5/4*c - (contains cid) ``` ```x3/2o3/2o3/2o5/4*a5/4*c - (contains "2doe") o3/2x3/2o3/2o5/4*a5/4*c - (contains "2gike") o3/2o3/2x3/2o5/4*a5/4*c - (contains cid) o3/2o3/2o3/2x5/4*a5/4*c - (contains cid) ``` otherWythoffians ```x3x3/2o3o5/4*a5*c - (contains "2doe") x3o3/2x3o5/4*a5*c - (contains "2seihid") x3o3/2o3x5/4*a5*c - [Grünbaumian] o3x3/2x3o5/4*a5*c - [Grünbaumian] o3x3/2o3x5/4*a5*c - o3o3/2x3x5/4*a5*c - (contains "2gidhei") x3x3/2x3o5/4*a5*c - [Grünbaumian] x3x3/2o3x5/4*a5*c - [Grünbaumian] x3o3/2x3x5/4*a5*c - [Grünbaumian] o3x3/2x3x5/4*a5*c - [Grünbaumian] x3x3/2x3x5/4*a5*c - [Grünbaumian] ``` ```x3/2x3/2o3o5*a5/4*c - [Grünbaumian] x3/2o3/2x3o5*a5/4*c - [Grünbaumian] x3/2o3/2o3x5*a5/4*c - stut xethi o3/2x3/2x3o5*a5/4*c - [Grünbaumian] o3/2x3/2o3x5*a5/4*c - o3/2o3/2x3x5*a5/4*c - (contains "2gidhei") x3/2x3/2x3o5*a5/4*c - [Grünbaumian] x3/2x3/2o3x5*a5/4*c - [Grünbaumian] x3/2o3/2x3x5*a5/4*c - [Grünbaumian] o3/2x3/2x3x5*a5/4*c - [Grünbaumian] x3/2x3/2x3x5*a5/4*c - [Grünbaumian] ``` ```x3x3o3/2o5/4*a5/4*c - (contains "2doe") x3o3x3/2o5/4*a5/4*c - [Grünbaumian] x3o3o3/2x5/4*a5/4*c - [Grünbaumian] o3x3x3/2o5/4*a5/4*c - (contains cid) o3x3o3/2x5/4*a5/4*c - o3o3x3/2x5/4*a5/4*c - [Grünbaumian] x3x3x3/2o5/4*a5/4*c - [Grünbaumian] x3x3o3/2x5/4*a5/4*c - [Grünbaumian] x3o3x3/2x5/4*a5/4*c - [Grünbaumian] o3x3x3/2x5/4*a5/4*c - [Grünbaumian] x3x3x3/2x5/4*a5/4*c - [Grünbaumian] ``` ```x3/2x3/2o3/2o5/4*a5/4*c - [Grünbaumian] x3/2o3/2x3/2o5/4*a5/4*c - [Grünbaumian] x3/2o3/2o3/2x5/4*a5/4*c - [Grünbaumian] o3/2x3/2x3/2o5/4*a5/4*c - [Grünbaumian] o3/2x3/2o3/2x5/4*a5/4*c - o3/2o3/2x3/2x5/4*a5/4*c - [Grünbaumian] x3/2x3/2x3/2o5/4*a5/4*c - [Grünbaumian] x3/2x3/2o3/2x5/4*a5/4*c - [Grünbaumian] x3/2o3/2x3/2x5/4*a5/4*c - [Grünbaumian] o3/2x3/2x3/2x5/4*a5/4*c - [Grünbaumian] x3/2x3/2x3/2x5/4*a5/4*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o3o5/3*a5/2*c   (up)

 o3o3o3o5/3*a5/2*c (µ=69) o3o3o3/2o5/2*a5/2*c (µ=171) o3/2o3o3o5/2*a5/3*c (µ=531) o3o3/2o3o5/2*a5/3*c (µ=669) quasiregulars ```x3o3o3o5/3*a5/2*c - (contains "2gissid") o3x3o3o5/3*a5/2*c - (contains "2ike") o3o3x3o5/3*a5/2*c - (contains gacid) o3o3o3x5/3*a5/2*c - (contains gacid) ``` ```x3o3o3/2o5/2*a5/2*c - (contains "2gissid") o3x3o3/2o5/2*a5/2*c - (contains "2ike") o3o3x3/2o5/2*a5/2*c - (contains gacid) o3o3o3/2x5/2*a5/2*c - (contains gacid) ``` ```x3/2o3o3o5/2*a5/3*c - (contains "2gissid") o3/2x3o3o5/2*a5/3*c - (contains "2ike") o3/2o3x3o5/2*a5/3*c - (contains gacid) o3/2o3o3x5/2*a5/3*c - (contains gacid) ``` ```x3o3/2o3o5/2*a5/3*c - (contains "2gissid") o3x3/2o3o5/2*a5/3*c - (contains "2ike") o3o3/2x3o5/2*a5/3*c - (contains gacid) o3o3/2o3x5/2*a5/3*c - (contains gacid) ``` otherWythoffians ```x3x3o3o5/3*a5/2*c - (contains "2gissid") x3o3x3o5/3*a5/2*c - [Grünbaumian] x3o3o3x5/3*a5/2*c - getit xethi o3x3x3o5/3*a5/2*c - (contains gacid) o3x3o3x5/3*a5/2*c - o3o3x3x5/3*a5/2*c - (contains "2sidhei") x3x3x3o5/3*a5/2*c - [Grünbaumian] x3x3o3x5/3*a5/2*c - gik vixathi x3o3x3x5/3*a5/2*c - [Grünbaumian] o3x3x3x5/3*a5/2*c - x3x3x3x5/3*a5/2*c - [Grünbaumian] ``` ```x3x3o3/2o5/2*a5/2*c - (contains "2gissid") x3o3x3/2o5/2*a5/2*c - [Grünbaumian] x3o3o3/2x5/2*a5/2*c - [Grünbaumian] o3x3x3/2o5/2*a5/2*c - (contains gacid) o3x3o3/2x5/2*a5/2*c - o3o3x3/2x5/2*a5/2*c - [Grünbaumian] x3x3x3/2o5/2*a5/2*c - [Grünbaumian] x3x3o3/2x5/2*a5/2*c - [Grünbaumian] x3o3x3/2x5/2*a5/2*c - [Grünbaumian] o3x3x3/2x5/2*a5/2*c - [Grünbaumian] x3x3x3/2x5/2*a5/2*c - [Grünbaumian] ``` ```x3/2x3o3o5/2*a5/3*c - [Grünbaumian] x3/2o3x3o5/2*a5/3*c - (contains "2geihid") x3/2o3o3x5/2*a5/3*c - [Grünbaumian] o3/2x3x3o5/2*a5/3*c - (contains gacid) o3/2x3o3x5/2*a5/3*c - o3/2o3x3x5/2*a5/3*c - (contains "2sidhei") x3/2x3x3o5/2*a5/3*c - [Grünbaumian] x3/2x3o3x5/2*a5/3*c - [Grünbaumian] x3/2o3x3x5/2*a5/3*c - [Grünbaumian] o3/2x3x3x5/2*a5/3*c - x3/2x3x3x5/2*a5/3*c - [Grünbaumian] ``` ```x3x3/2o3o5/2*a5/3*c - (contains "2gissid") x3o3/2x3o5/2*a5/3*c - (contains "2geihid") x3o3/2o3x5/2*a5/3*c - [Grünbaumian] o3x3/2x3o5/2*a5/3*c - [Grünbaumian] o3x3/2o3x5/2*a5/3*c - o3o3/2x3x5/2*a5/3*c - (contains "2sidhei") x3x3/2x3o5/2*a5/3*c - [Grünbaumian] x3x3/2o3x5/2*a5/3*c - [Grünbaumian] x3o3/2x3x5/2*a5/3*c - [Grünbaumian] o3x3/2x3x5/2*a5/3*c - [Grünbaumian] x3x3/2x3x5/2*a5/3*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o3/2o3o5/3*a5/2*c (µ=1131) o3o3/2o3/2o5/3*a5/3*c (µ=1491) o3/2o3/2o3/2o5/2*a5/2*c (µ=1509) o3/2o3o3/2o5/3*a5/3*c (µ=1629) quasiregulars ```x3/2o3/2o3o5/3*a5/2*c - (contains "2gissid") o3/2x3/2o3o5/3*a5/2*c - (contains "2ike") o3/2o3/2x3o5/3*a5/2*c - (contains gacid) o3/2o3/2o3x5/3*a5/2*c - (contains gacid) ``` ```x3o3/2o3/2o5/3*a5/3*c - (contains "2gissid") o3x3/2o3/2o5/3*a5/3*c - (contains "2ike") o3o3/2x3/2o5/3*a5/3*c - (contains gacid) o3o3/2o3/2x5/3*a5/3*c - (contains gacid) ``` ```x3/2o3/2o3/2o5/2*a5/2*c - (contains "2gissid") o3/2x3/2o3/2o5/2*a5/2*c - (contains "2ike") o3/2o3/2x3/2o5/2*a5/2*c - (contains gacid) o3/2o3/2o3/2x5/2*a5/2*c - (contains gacid) ``` ```x3/2o3o3/2o5/3*a5/3*c - (contains "2gissid") o3/2x3o3/2o5/3*a5/3*c - (contains "2ike") o3/2o3x3/2o5/3*a5/3*c - (contains gacid) o3/2o3o3/2x5/3*a5/3*c - (contains gacid) ``` otherWythoffians ```x3/2x3/2o3o5/3*a5/2*c - [Grünbaumian] x3/2o3/2x3o5/3*a5/2*c - [Grünbaumian] x3/2o3/2o3x5/3*a5/2*c - getit xethi o3/2x3/2x3o5/3*a5/2*c - [Grünbaumian] o3/2x3/2o3x5/3*a5/2*c - o3/2o3/2x3x5/3*a5/2*c - (contains "2sidhei") x3/2x3/2x3o5/3*a5/2*c - [Grünbaumian] x3/2x3/2o3x5/3*a5/2*c - [Grünbaumian] x3/2o3/2x3x5/3*a5/2*c - [Grünbaumian] o3/2x3/2x3x5/3*a5/2*c - [Grünbaumian] x3/2x3/2x3x5/3*a5/2*c - [Grünbaumian] ``` ```x3x3/2o3/2o5/3*a5/3*c - (contains "2gissid") x3o3/2x3/2o5/3*a5/3*c - (contains "2geihid") x3o3/2o3/2x5/3*a5/3*c - getit xethi o3x3/2x3/2o5/3*a5/3*c - [Grünbaumian] o3x3/2o3/2x5/3*a5/3*c - o3o3/2x3/2x5/3*a5/3*c - [Grünbaumian] x3x3/2x3/2o5/3*a5/3*c - [Grünbaumian] x3x3/2o3/2x5/3*a5/3*c - gik vixathi x3o3/2x3/2x5/3*a5/3*c - [Grünbaumian] o3x3/2x3/2x5/3*a5/3*c - [Grünbaumian] x3x3/2x3/2x5/3*a5/3*c - [Grünbaumian] ``` ```x3/2x3/2o3/2o5/2*a5/2*c - [Grünbaumian] x3/2o3/2x3/2o5/2*a5/2*c - [Grünbaumian] x3/2o3/2o3/2x5/2*a5/2*c - [Grünbaumian] o3/2x3/2x3/2o5/2*a5/2*c - [Grünbaumian] o3/2x3/2o3/2x5/2*a5/2*c - o3/2o3/2x3/2x5/2*a5/2*c - [Grünbaumian] x3/2x3/2x3/2o5/2*a5/2*c - [Grünbaumian] x3/2x3/2o3/2x5/2*a5/2*c - [Grünbaumian] x3/2o3/2x3/2x5/2*a5/2*c - [Grünbaumian] o3/2x3/2x3/2x5/2*a5/2*c - [Grünbaumian] x3/2x3/2x3/2x5/2*a5/2*c - [Grünbaumian] ``` ```x3/2x3o3/2o5/3*a5/3*c - [Grünbaumian] x3/2o3x3/2o5/3*a5/3*c - (contains "2geihid") x3/2o3o3/2x5/3*a5/3*c - getit xethi o3/2x3x3/2o5/3*a5/3*c - (contains gacid) o3/2x3o3/2x5/3*a5/3*c - o3/2o3x3/2x5/3*a5/3*c - [Grünbaumian] x3/2x3x3/2o5/3*a5/3*c - [Grünbaumian] x3/2x3o3/2x5/3*a5/3*c - [Grünbaumian] x3/2o3x3/2x5/3*a5/3*c - [Grünbaumian] o3/2x3x3/2x5/3*a5/3*c - [Grünbaumian] x3/2x3x3/2x5/3*a5/3*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3/2o3o3o5/3*a5*c   (up)

 o3/2o3o3o5/3*a5*c (µ=181) o3o3/2o3o5/3*a5*c (µ=299) o3o3o3o5/2*a5/4*c (µ=419) o3o3/2o3/2o5/2*a5*c (µ=421) quasiregulars ```x3/2o3o3o5/3*a5*c - gardatady+1440{5} o3/2x3o3o5/3*a5*c - (contains "2gike") o3/2o3x3o5/3*a5*c - (contains cid) o3/2o3o3x5/3*a5*c - (contains gacid) ``` ```x3o3/2o3o5/3*a5*c - gardatady+1440{5} o3x3/2o3o5/3*a5*c - (contains "2gike") o3o3/2x3o5/3*a5*c - (contains cid) o3o3/2o3x5/3*a5*c - (contains gacid) ``` ```x3o3o3o5/2*a5/4*c - gardatady+1440{5} o3x3o3o5/2*a5/4*c - (contains "2gike") o3o3x3o5/2*a5/4*c - (contains cid) o3o3o3x5/2*a5/4*c - (contains gacid) ``` ```x3o3/2o3/2o5/2*a5*c - gardatady+1440{5} o3x3/2o3/2o5/2*a5*c - (contains "2gike") o3o3/2x3/2o5/2*a5*c - (contains cid) o3o3/2o3/2x5/2*a5*c - (contains gacid) ``` otherWythoffians ```x3/2x3o3o5/3*a5*c - [Grünbaumian] x3/2o3x3o5/3*a5*c - (contains "2seihid") x3/2o3o3x5/3*a5*c - git thixady o3/2x3x3o5/3*a5*c - (contains cid) o3/2x3o3x5/3*a5*c - o3/2o3x3x5/3*a5*c - gefirdit xethi x3/2x3x3o5/3*a5*c - [Grünbaumian] x3/2x3o3x5/3*a5*c - [Grünbaumian] x3/2o3x3x5/3*a5*c - (contains "2seihid") o3/2x3x3x5/3*a5*c - x3/2x3x3x5/3*a5*c - [Grünbaumian] ``` ```x3x3/2o3o5/3*a5*c - getit thix x3o3/2x3o5/3*a5*c - (contains "2seihid") x3o3/2o3x5/3*a5*c - git thixady o3x3/2x3o5/3*a5*c - [Grünbaumian] o3x3/2o3x5/3*a5*c - o3o3/2x3x5/3*a5*c - gefirdit xethi x3x3/2x3o5/3*a5*c - [Grünbaumian] x3x3/2o3x5/3*a5*c - x3o3/2x3x5/3*a5*c - (contains "2seihid") o3x3/2x3x5/3*a5*c - [Grünbaumian] x3x3/2x3x5/3*a5*c - [Grünbaumian] ``` ```x3x3o3o5/2*a5/4*c - getit thix x3o3x3o5/2*a5/4*c - [Grünbaumian] x3o3o3x5/2*a5/4*c - [Grünbaumian] o3x3x3o5/2*a5/4*c - (contains cid) o3x3o3x5/2*a5/4*c - o3o3x3x5/2*a5/4*c - gefirdit xethi x3x3x3o5/2*a5/4*c - [Grünbaumian] x3x3o3x5/2*a5/4*c - [Grünbaumian] x3o3x3x5/2*a5/4*c - [Grünbaumian] o3x3x3x5/2*a5/4*c - x3x3x3x5/2*a5/4*c - [Grünbaumian] ``` ```x3x3/2o3/2o5/2*a5*c - getit thix x3o3/2x3/2o5/2*a5*c - (contains "2seihid") x3o3/2o3/2x5/2*a5*c - [Grünbaumian] o3x3/2x3/2o5/2*a5*c - [Grünbaumian] o3x3/2o3/2x5/2*a5*c - o3o3/2x3/2x5/2*a5*c - [Grünbaumian] x3x3/2x3/2o5/2*a5*c - [Grünbaumian] x3x3/2o3/2x5/2*a5*c - [Grünbaumian] x3o3/2x3/2x5/2*a5*c - [Grünbaumian] o3x3/2x3/2x5/2*a5*c - [Grünbaumian] x3x3/2x3/2x5/2*a5*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o3o3/2o5/2*a5*c (µ=539) o3o3o3/2o5/3*a5/4*c (µ=1261) o3/2o3/2o3o5/2*a5/4*c (µ=1501) o3/2o3/2o3/2o5/3*a5/4*c (µ=2579) quasiregulars ```x3/2o3o3/2o5/2*a5*c - gardatady+1440{5} o3/2x3o3/2o5/2*a5*c - (contains "2gike") o3/2o3x3/2o5/2*a5*c - (contains cid) o3/2o3o3/2x5/2*a5*c - (contains gacid) ``` ```x3o3o3/2o5/3*a5/4*c - gardatady+1440{5} o3x3o3/2o5/3*a5/4*c - (contains "2gike") o3o3x3/2o5/3*a5/4*c - (contains cid) o3o3o3/2x5/3*a5/4*c - (contains gacid) ``` ```x3/2o3/2o3o5/2*a5/4*c - gardatady+1440{5} o3/2x3/2o3o5/2*a5/4*c - (contains "2gike") o3/2o3/2x3o5/2*a5/4*c - (contains cid) o3/2o3/2o3x5/2*a5/4*c - (contains gacid) ``` ```x3/2o3/2o3/2o5/3*a5/4*c - gardatady+1440{5} o3/2x3/2o3/2o5/3*a5/4*c - (contains "2gike") o3/2o3/2x3/2o5/3*a5/4*c - (contains cid) o3/2o3/2o3/2x5/3*a5/4*c - (contains gacid) ``` otherWythoffians ```x3/2x3o3/2o5/2*a5*c - [Grünbaumian] x3/2o3x3/2o5/2*a5*c - (contains "2seihid") x3/2o3o3/2x5/2*a5*c - [Grünbaumian] o3/2x3x3/2o5/2*a5*c - (contains cid) o3/2x3o3/2x5/2*a5*c - o3/2o3x3/2x5/2*a5*c - [Grünbaumian] x3/2x3x3/2o5/2*a5*c - [Grünbaumian] x3/2x3o3/2x5/2*a5*c - [Grünbaumian] x3/2o3x3/2x5/2*a5*c - [Grünbaumian] o3/2x3x3/2x5/2*a5*c - [Grünbaumian] x3/2x3x3/2x5/2*a5*c - [Grünbaumian] ``` ```x3x3o3/2o5/3*a5/4*c - getit thix x3o3x3/2o5/3*a5/4*c - [Grünbaumian] x3o3o3/2x5/3*a5/4*c - git thixady o3x3x3/2o5/3*a5/4*c - (contains cid) o3x3o3/2x5/3*a5/4*c - o3o3x3/2x5/3*a5/4*c - [Grünbaumian] x3x3x3/2o5/3*a5/4*c - [Grünbaumian] x3x3o3/2x5/3*a5/4*c - x3o3x3/2x5/3*a5/4*c - [Grünbaumian] o3x3x3/2x5/3*a5/4*c - [Grünbaumian] x3x3x3/2x5/3*a5/4*c - [Grünbaumian] ``` ```x3/2x3/2o3o5/2*a5/4*c - [Grünbaumian] x3/2o3/2x3o5/2*a5/4*c - [Grünbaumian] x3/2o3/2o3x5/2*a5/4*c - [Grünbaumian] o3/2x3/2x3o5/2*a5/4*c - [Grünbaumian] o3/2x3/2o3x5/2*a5/4*c - o3/2o3/2x3x5/2*a5/4*c - gefirdit xethi x3/2x3/2x3o5/2*a5/4*c - [Grünbaumian] x3/2x3/2o3x5/2*a5/4*c - [Grünbaumian] x3/2o3/2x3x5/2*a5/4*c - [Grünbaumian] o3/2x3/2x3x5/2*a5/4*c - [Grünbaumian] x3/2x3/2x3x5/2*a5/4*c - [Grünbaumian] ``` ```x3/2x3/2o3/2o5/3*a5/4*c - [Grünbaumian] x3/2o3/2x3/2o5/3*a5/4*c - [Grünbaumian] x3/2o3/2o3/2x5/3*a5/4*c - git thixady o3/2x3/2x3/2o5/3*a5/4*c - [Grünbaumian] o3/2x3/2o3/2x5/3*a5/4*c - o3/2o3/2x3/2x5/3*a5/4*c - [Grünbaumian] x3/2x3/2x3/2o5/3*a5/4*c - [Grünbaumian] x3/2x3/2o3/2x5/3*a5/4*c - [Grünbaumian] x3/2o3/2x3/2x5/3*a5/4*c - [Grünbaumian] o3/2x3/2x3/2x5/3*a5/4*c - [Grünbaumian] x3/2x3/2x3/2x5/3*a5/4*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o3/2o5*a5/2*c   (up)

 o3o3o3/2o5*a5/2*c (µ=11) o3o3/2o3o5*a5/3*c (µ=109) o3o3o3o5/4*a5/2*c (µ=229) o3/2o3o3o5*a5/3*c (µ=371) quasiregulars ```x3o3o3/2o5*a5/2*c - sirdatady+1440{5/2} o3x3o3/2o5*a5/2*c - (contains "2ike") o3o3x3/2o5*a5/2*c - (contains gacid) o3o3o3/2x5*a5/2*c - (contains cid) ``` ```o3o3/2o3o5*a5/3*c - sirdatady+1440{5/2} o3x3/2o3o5*a5/3*c - (contains "2ike") o3o3/2x3o5*a5/3*c - (contains gacid) o3o3/2o3x5*a5/3*c - (contains cid) ``` ```x3o3o3o5/4*a5/2*c - sirdatady+1440{5/2} o3x3o3o5/4*a5/2*c - (contains "2ike") o3o3x3o5/4*a5/2*c - (contains gacid) o3o3o3x5/4*a5/2*c - (contains cid) ``` ```x3/2o3o3o5*a5/3*c - sirdatady+1440{5/2} o3/2x3o3o5*a5/3*c - (contains "2ike") o3/2o3x3o5*a5/3*c - (contains gacid) o3/2o3o3x5*a5/3*c - (contains cid) ``` otherWythoffians ```x3x3o3/2o5*a5/2*c - stut thix x3o3x3/2o5*a5/2*c - [Grünbaumian] x3o3o3/2x5*a5/2*c - sit thixady o3x3x3/2o5*a5/2*c - (contains gacid) o3x3o3/2x5*a5/2*c - o3o3x3/2x5*a5/2*c - [Grünbaumian] x3x3x3/2o5*a5/2*c - [Grünbaumian] x3x3o3/2x5*a5/2*c - x3o3x3/2x5*a5/2*c - [Grünbaumian] o3x3x3/2x5*a5/2*c - [Grünbaumian] x3x3x3/2x5*a5/2*c - [Grünbaumian] ``` ```x3x3/2o3o5*a5/3*c - stut thix x3o3/2x3o5*a5/3*c - (contains "2geihid") x3o3/2o3x5*a5/3*c - sit thixady o3x3/2x3o5*a5/3*c - [Grünbaumian] o3x3/2o3x5*a5/3*c - o3o3/2x3x5*a5/3*c - gefridit xethi x3x3/2x3o5*a5/3*c - [Grünbaumian] x3x3/2o3x5*a5/3*c - x3o3/2x3x5*a5/3*c - (contains "2geihid") o3x3/2x3x5*a5/3*c - [Grünbaumian] x3x3/2x3x5*a5/3*c - [Grünbaumian] ``` ```x3x3o3o5/4*a5/2*c - stut thix x3o3x3o5/4*a5/2*c - [Grünbaumian] x3o3o3x5/4*a5/2*c - [Grünbaumian] o3x3x3o5/4*a5/2*c - (contains gacid) o3x3o3x5/4*a5/2*c - o3o3x3x5/4*a5/2*c - gefridit xethi x3x3x3o5/4*a5/2*c - [Grünbaumian] x3x3o3x5/4*a5/2*c - [Grünbaumian] x3o3x3x5/4*a5/2*c - [Grünbaumian] o3x3x3x5/4*a5/2*c - x3x3x3x5/4*a5/2*c - [Grünbaumian] ``` ```x3/2x3o3o5*a5/3*c - [Grünbaumian] x3/2o3x3o5*a5/3*c - (contains "2geihid") x3/2o3o3x5*a5/3*c - sit thixady o3/2x3x3o5*a5/3*c - (contains gacid) o3/2x3o3x5*a5/3*c - o3/2o3x3x5*a5/3*c - gefridit xethi x3/2x3x3o5*a5/3*c - [Grünbaumian] x3/2x3o3x5*a5/3*c - [Grünbaumian] x3/2o3x3x5*a5/3*c - (contains "2geihid") o3/2x3x3x5*a5/3*c - x3/2x3x3x5*a5/3*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o3/2o3/2o5*a5/2*c (µ=949) o3/2o3/2o3o5/4*a5/2*c (µ=1691) o3/2o3o3/2o5/4*a5/3*c (µ=1789) o3o3/2o3/2o5/4*a5/3*c (µ=2051) quasiregulars ```x3/2o3/2o3/2o5*a5/2*c - sirdatady+1440{5/2} o3/2x3/2o3/2o5*a5/2*c - (contains "2ike") o3/2o3/2x3/2o5*a5/2*c - (contains gacid) o3/2o3/2o3/2x5*a5/2*c - (contains cid) ``` ```x3/2o3/2o3o5/4*a5/2*c - sirdatady+1440{5/2} o3/2x3/2o3o5/4*a5/2*c - (contains "2ike") o3/2o3/2x3o5/4*a5/2*c - (contains gacid) o3/2o3/2o3x5/4*a5/2*c - (contains cid) ``` ```x3/2o3o3/2o5/4*a5/3*c - sirdatady+1440{5/2} o3/2x3o3/2o5/4*a5/3*c - (contains "2ike") o3/2o3x3/2o5/4*a5/3*c - (contains gacid) o3/2o3o3/2x5/4*a5/3*c - (contains cid) ``` ```x3o3/2o3/2o5/4*a5/3*c - sirdatady+1440{5/2} o3x3/2o3/2o5/4*a5/3*c - (contains "2ike") o3o3/2x3/2o5/4*a5/3*c - (contains gacid) o3o3/2o3/2x5/4*a5/3*c - (contains cid) ``` otherWythoffians ```x3/2x3/2o3/2o5*a5/2*c - [Grünbaumian] x3/2o3/2x3/2o5*a5/2*c - [Grünbaumian] x3/2o3/2o3/2x5*a5/2*c - sit thixady o3/2x3/2x3/2o5*a5/2*c - [Grünbaumian] o3/2x3/2o3/2x5*a5/2*c - o3/2o3/2x3/2x5*a5/2*c - [Grünbaumian] x3/2x3/2x3/2o5*a5/2*c - [Grünbaumian] x3/2x3/2o3/2x5*a5/2*c - [Grünbaumian] x3/2o3/2x3/2x5*a5/2*c - [Grünbaumian] o3/2x3/2x3/2x5*a5/2*c - [Grünbaumian] x3/2x3/2x3/2x5*a5/2*c - [Grünbaumian] ``` ```x3/2x3/2o3o5/4*a5/2*c - [Grünbaumian] x3/2o3/2x3o5/4*a5/2*c - [Grünbaumian] x3/2o3/2o3x5/4*a5/2*c - [Grünbaumian] o3/2x3/2x3o5/4*a5/2*c - [Grünbaumian] o3/2x3/2o3x5/4*a5/2*c - o3/2o3/2x3x5/4*a5/2*c - gefridit xethi x3/2x3/2x3o5/4*a5/2*c - [Grünbaumian] x3/2x3/2o3x5/4*a5/2*c - [Grünbaumian] x3/2o3/2x3x5/4*a5/2*c - [Grünbaumian] o3/2x3/2x3x5/4*a5/2*c - [Grünbaumian] x3/2x3/2x3x5/4*a5/2*c - [Grünbaumian] ``` ```x3/2x3o3/2o5/4*a5/3*c - [Grünbaumian] x3/2o3x3/2o5/4*a5/3*c - (contains "2geihid") x3/2o3o3/2x5/4*a5/3*c - [Grünbaumian] o3/2x3x3/2o5/4*a5/3*c - (contains gacid) o3/2x3o3/2x5/4*a5/3*c - o3/2o3x3/2x5/4*a5/3*c - [Grünbaumian] x3/2x3x3/2o5/4*a5/3*c - [Grünbaumian] x3/2x3o3/2x5/4*a5/3*c - [Grünbaumian] x3/2o3x3/2x5/4*a5/3*c - [Grünbaumian] o3/2x3x3/2x5/4*a5/3*c - [Grünbaumian] x3/2x3x3/2x5/4*a5/3*c - [Grünbaumian] ``` ```x3x3/2o3/2o5/4*a5/3*c - stut thix x3o3/2x3/2o5/4*a5/3*c - (contains "2geihid") x3o3/2o3/2x5/4*a5/3*c - [Grünbaumian] o3x3/2x3/2o5/4*a5/3*c - [Grünbaumian] o3x3/2o3/2x5/4*a5/3*c - o3o3/2x3/2x5/4*a5/3*c - [Grünbaumian] x3x3/2x3/2o5/4*a5/3*c - [Grünbaumian] x3x3/2o3/2x5/4*a5/3*c - [Grünbaumian] x3o3/2x3/2x5/4*a5/3*c - [Grünbaumian] o3x3/2x3/2x5/4*a5/3*c - [Grünbaumian] x3x3/2x3/2x5/4*a5/3*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3/2o5o5/2o3/2*a5*c   (up)

 o3/2o5o5/2o3/2*a5*c (µ=113) o3/2o5o5/3o3*a5*c (µ=127) o3o5o5/2o3*a5/4*c (µ=247) o3o5/4o5/3o3*a5*c (µ=353) quasiregulars ```x3/2o5o5/2o3/2*a5*c - (contains cid) o3/2x5o5/2o3/2*a5*c - (contains cid) o3/2o5x5/2o3/2*a5*c - (contains "2doe") o3/2o5o5/2x3/2*a5*c - (contains gacid) ``` ```x3/2o5o5/3o3*a5*c - (contains cid) o3/2x5o5/3o3*a5*c - (contains cid) o3/2o5x5/3o3*a5*c - (contains "2doe") o3/2o5o5/3x3*a5*c - (contains gacid) ``` ```x3o5o5/2o3*a5/4*c - (contains cid) o3x5o5/2o3*a5/4*c - (contains cid) o3o5x5/2o3*a5/4*c - (contains "2doe") o3o5o5/2x3*a5/4*c - (contains gacid) ``` ```x3o5/4o5/3o3*a5*c - (contains cid) o3x5/4o5/3o3*a5*c - (contains cid) o3o5/4x5/3o3*a5*c - (contains "2doe") o3o5/4o5/3x3*a5*c - (contains gacid) ``` otherWythoffians ```x3/2x5o5/2o3/2*a5*c - [Grünbaumian] x3/2o5x5/2o3/2*a5*c - raffixthi x3/2o5o5/2x3/2*a5*c - [Grünbaumian] o3/2x5x5/2o3/2*a5*c - sefradit thix o3/2x5o5/2x3/2*a5*c - o3/2o5x5/2x3/2*a5*c - [Grünbaumian] x3/2x5x5/2o3/2*a5*c - [Grünbaumian] x3/2x5o5/2x3/2*a5*c - [Grünbaumian] x3/2o5x5/2x3/2*a5*c - [Grünbaumian] o3/2x5x5/2x3/2*a5*c - [Grünbaumian] x3/2x5x5/2x3/2*a5*c - [Grünbaumian] ``` ```x3/2x5o5/3o3*a5*c - [Grünbaumian] x3/2o5x5/3o3*a5*c - raffixthi x3/2o5o5/3x3*a5*c - (contains cid) o3/2x5x5/3o3*a5*c - sefradit thix o3/2x5o5/3x3*a5*c - o3/2o5x5/3x3*a5*c - (contains "2doe") x3/2x5x5/3o3*a5*c - [Grünbaumian] x3/2x5o5/3x3*a5*c - [Grünbaumian] x3/2o5x5/3x3*a5*c - hixquitixhi o3/2x5x5/3x3*a5*c - x3/2x5x5/3x3*a5*c - [Grünbaumian] ``` ```x3x5o5/2o3*a5/4*c - (contains cid) x3o5x5/2o3*a5/4*c - [Grünbaumian] x3o5o5/2x3*a5/4*c - (contains cid) o3x5x5/2o3*a5/4*c - sefradit thix o3x5o5/2x3*a5/4*c - o3o5x5/2x3*a5/4*c - [Grünbaumian] x3x5x5/2o3*a5/4*c - [Grünbaumian] x3x5o5/2x3*a5/4*c - x3o5x5/2x3*a5/4*c - [Grünbaumian] o3x5x5/2x3*a5/4*c - [Grünbaumian] x3x5x5/2x3*a5/4*c - [Grünbaumian] ``` ```x3x5/4o5/3o3*a5*c - (contains cid) x3o5/4x5/3o3*a5*c - raffixthi x3o5/4o5/3x3*a5*c - (contains cid) o3x5/4x5/3o3*a5*c - [Grünbaumian] o3x5/4o5/3x3*a5*c - o3o5/4x5/3x3*a5*c - (contains "2doe") x3x5/4x5/3o3*a5*c - [Grünbaumian] x3x5/4o5/3x3*a5*c - x3o5/4x5/3x3*a5*c - hixquitixhi o3x5/4x5/3x3*a5*c - [Grünbaumian] x3x5/4x5/3x3*a5*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3o5/4o5/2o3/2*a5*c (µ=847) o3o5o5/3o3/2*a5/4*c (µ=953) o3/2o5/4o5/2o3*a5/4*c (µ=1673) o3/2o5/4o5/3o3/2*a5/4*c (µ=2887) quasiregulars ```x3o5/4o5/2o3/2*a5*c - (contains cid) o3x5/4o5/2o3/2*a5*c - (contains cid) o3o5/4x5/2o3/2*a5*c - (contains "2doe") o3o5/4o5/2x3/2*a5*c - (contains gacid) ``` ```x3o5o5/3o3/2*a5/4*c - (contains cid) o3x5o5/3o3/2*a5/4*c - (contains cid) o3o5x5/3o3/2*a5/4*c - (contains "2doe") o3o5o5/3x3/2*a5/4*c - (contains gacid) ``` ```x3/2o5/4o5/2o3*a5/4*c - (contains cid) o3/2x5/4o5/2o3*a5/4*c - (contains cid) o3/2o5/4x5/2o3*a5/4*c - (contains "2doe") o3/2o5/4o5/2x3*a5/4*c - (contains gacid) ``` ```x3/2o5/4o5/3o3/2*a5/4*c - (contains cid) o3/2x5/4o5/3o3/2*a5/4*c - (contains cid) o3/2o5/4x5/3o3/2*a5/4*c - (contains "2doe") o3/2o5/4o5/3x3/2*a5/4*c - (contains gacid) ``` otherWythoffians ```x3x5/4o5/2o3/2*a5*c - (contains cid) x3o5/4x5/2o3/2*a5*c - raffixthi x3o5/4o5/2x3/2*a5*c - [Grünbaumian] o3x5/4x5/2o3/2*a5*c - [Grünbaumian] o3x5/4o5/2x3/2*a5*c - o3o5/4x5/2x3/2*a5*c - [Grünbaumian] x3x5/4x5/2o3/2*a5*c - [Grünbaumian] x3x5/4o5/2x3/2*a5*c - [Grünbaumian] x3o5/4x5/2x3/2*a5*c - [Grünbaumian] o3x5/4x5/2x3/2*a5*c - [Grünbaumian] x3x5/4x5/2x3/2*a5*c - [Grünbaumian] ``` ```x3x5o5/3o3/2*a5/4*c - (contains cid) x3o5x5/3o3/2*a5/4*c - [Grünbaumian] x3o5o5/3x3/2*a5/4*c - [Grünbaumian] o3x5x5/3o3/2*a5/4*c - sefradit thix o3x5o5/3x3/2*a5/4*c - o3o5x5/3x3/2*a5/4*c - (contains "2doe") x3x5x5/3o3/2*a5/4*c - [Grünbaumian] x3x5o5/3x3/2*a5/4*c - [Grünbaumian] x3o5x5/3x3/2*a5/4*c - [Grünbaumian] o3x5x5/3x3/2*a5/4*c - x3x5x5/3x3/2*a5/4*c - [Grünbaumian] ``` ```x3/2x5/4o5/2o3*a5/4*c - [Grünbaumian] x3/2o5/4x5/2o3*a5/4*c - [Grünbaumian] x3/2o5/4o5/2x3*a5/4*c - (contains cid) o3/2x5/4x5/2o3*a5/4*c - [Grünbaumian] o3/2x5/4o5/2x3*a5/4*c - o3/2o5/4x5/2x3*a5/4*c - [Grünbaumian] x3/2x5/4x5/2o3*a5/4*c - [Grünbaumian] x3/2x5/4o5/2x3*a5/4*c - [Grünbaumian] x3/2o5/4x5/2x3*a5/4*c - [Grünbaumian] o3/2x5/4x5/2x3*a5/4*c - [Grünbaumian] x3/2x5/4x5/2x3*a5/4*c - [Grünbaumian] ``` ```x3/2x5/4o5/3o3/2*a5/4*c - [Grünbaumian] x3/2o5/4x5/3o3/2*a5/4*c - [Grünbaumian] x3/2o5/4o5/3x3/2*a5/4*c - [Grünbaumian] o3/2x5/4x5/3o3/2*a5/4*c - [Grünbaumian] o3/2x5/4o5/3x3/2*a5/4*c - o3/2o5/4x5/3x3/2*a5/4*c - (contains "2doe") x3/2x5/4x5/3o3/2*a5/4*c - [Grünbaumian] x3/2x5/4o5/3x3/2*a5/4*c - [Grünbaumian] x3/2o5/4x5/3x3/2*a5/4*c - [Grünbaumian] o3/2x5/4x5/3x3/2*a5/4*c - [Grünbaumian] x3/2x5/4x5/3x3/2*a5/4*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5o5/2o3*a5/3*c   (up)

 o3o5o5/2o3*a5/3*c (µ=17) o3/2o5o5/2o3/2*a5/2*c (µ=343) o3o5o5/3o3/2*a5/3*c (µ=463) o3o5/4o5/3o3*a5/2*c (µ=583) quasiregulars ```x3o5o5/2o3*a5/3*c - (contains gacid) o3x5o5/2o3*a5/3*c - (contains cid) o3o5x5/2o3*a5/3*c - (contains "2gissid") o3o5o5/2x3*a5/3*c - (contains gacid) ``` ```x3/2o5o5/2o3/2*a5/2*c - (contains gacid) o3/2x5o5/2o3/2*a5/2*c - (contains cid) o3/2o5x5/2o3/2*a5/2*c - (contains "2gissid") o3/2o5o5/2x3/2*a5/2*c - (contains gacid) ``` ```x3o5o5/3o3/2*a5/3*c - (contains gacid) o3x5o5/3o3/2*a5/3*c - (contains cid) o3o5x5/3o3/2*a5/3*c - (contains "2gissid") o3o5o5/3x3/2*a5/3*c - (contains gacid) ``` ```x3o5/4o5/3o3*a5/2*c - (contains gacid) o3x5/4o5/3o3*a5/2*c - (contains cid) o3o5/4x5/3o3*a5/2*c - (contains "2gissid") o3o5/4o5/3x3*a5/2*c - (contains gacid) ``` otherWythoffians ```x3x5o5/2o3*a5/3*c - (contains gacid) x3o5x5/2o3*a5/3*c - affixthi x3o5o5/2x3*a5/3*c - (contains gacid) o3x5x5/2o3*a5/3*c - (contains "2gissid") o3x5o5/2x3*a5/3*c - o3o5x5/2x3*a5/3*c - [Grünbaumian] x3x5x5/2o3*a5/3*c - hixtixhi x3x5o5/2x3*a5/3*c - x3o5x5/2x3*a5/3*c - [Grünbaumian] o3x5x5/2x3*a5/3*c - [Grünbaumian] x3x5x5/2x3*a5/3*c - [Grünbaumian] ``` ```x3/2x5o5/2o3/2*a5/2*c - [Grünbaumian] x3/2o5x5/2o3/2*a5/2*c - [Grünbaumian] x3/2o5o5/2x3/2*a5/2*c - [Grünbaumian] o3/2x5x5/2o3/2*a5/2*c - (contains "2gissid") o3/2x5o5/2x3/2*a5/2*c - o3/2o5x5/2x3/2*a5/2*c - [Grünbaumian] x3/2x5x5/2o3/2*a5/2*c - [Grünbaumian] x3/2x5o5/2x3/2*a5/2*c - [Grünbaumian] x3/2o5x5/2x3/2*a5/2*c - [Grünbaumian] o3/2x5x5/2x3/2*a5/2*c - [Grünbaumian] x3/2x5x5/2x3/2*a5/2*c - [Grünbaumian] ``` ```x3x5o5/3o3/2*a5/3*c - (contains gacid) x3o5x5/3o3/2*a5/3*c - affixthi x3o5o5/3x3/2*a5/3*c - [Grünbaumian] o3x5x5/3o3/2*a5/3*c - (contains "2gissid") o3x5o5/3x3/2*a5/3*c - o3o5x5/3x3/2*a5/3*c - gefradit thix x3x5x5/3o3/2*a5/3*c - hixtixhi x3x5o5/3x3/2*a5/3*c - [Grünbaumian] x3o5x5/3x3/2*a5/3*c - [Grünbaumian] o3x5x5/3x3/2*a5/3*c - x3x5x5/3x3/2*a5/3*c - [Grünbaumian] ``` ```x3x5/4o5/3o3*a5/2*c - (contains gacid) x3o5/4x5/3o3*a5/2*c - [Grünbaumian] x3o5/4o5/3x3*a5/2*c - (contains gacid) o3x5/4x5/3o3*a5/2*c - [Grünbaumian] o3x5/4o5/3x3*a5/2*c - o3o5/4x5/3x3*a5/2*c - gefradit thix x3x5/4x5/3o3*a5/2*c - [Grünbaumian] x3x5/4o5/3x3*a5/2*c - x3o5/4x5/3x3*a5/2*c - [Grünbaumian] o3x5/4x5/3x3*a5/2*c - [Grünbaumian] x3x5/4x5/3x3*a5/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o5o5/3o3*a5/2*c (µ=617) o3/2o5/4o5/2o3*a5/3*c (µ=1183) o3o5/4o5/2o3/2*a5/2*c (µ=1337) o3/2o5/4o5/3o3/2*a5/3*c (µ=2657) quasiregulars ```x3/2o5o5/3o3*a5/2*c - (contains gacid) o3/2x5o5/3o3*a5/2*c - (contains cid) o3/2o5x5/3o3*a5/2*c - (contains "2gissid") o3/2o5o5/3x3*a5/2*c - (contains gacid) ``` ```x3/2o5/4o5/2o3*a5/3*c - (contains gacid) o3/2x5/4o5/2o3*a5/3*c - (contains cid) o3/2o5/4x5/2o3*a5/3*c - (contains "2gissid") o3/2o5/4o5/2x3*a5/3*c - (contains gacid) ``` ```x3o5/4o5/2o3/2*a5/2*c - (contains gacid) o3x5/4o5/2o3/2*a5/2*c - (contains cid) o3o5/4x5/2o3/2*a5/2*c - (contains "2gissid") o3o5/4o5/2x3/2*a5/2*c - (contains gacid) ``` ```x3/2o5/4o5/3o3/2*a5/3*c - (contains gacid) o3/2x5/4o5/3o3/2*a5/3*c - (contains cid) o3/2o5/4x5/3o3/2*a5/3*c - (contains "2gissid") o3/2o5/4o5/3x3/2*a5/3*c - (contains gacid) ``` otherWythoffians ```x3/2x5o5/3o3*a5/2*c - [Grünbaumian] x3/2o5x5/3o3*a5/2*c - [Grünbaumian] x3/2o5o5/3x3*a5/2*c - (contains gacid) o3/2x5x5/3o3*a5/2*c - (contains "2gissid") o3/2x5o5/3x3*a5/2*c - o3/2o5x5/3x3*a5/2*c - gefradit thix x3/2x5x5/3o3*a5/2*c - [Grünbaumian] x3/2x5o5/3x3*a5/2*c - [Grünbaumian] x3/2o5x5/3x3*a5/2*c - [Grünbaumian] o3/2x5x5/3x3*a5/2*c - x3/2x5x5/3x3*a5/2*c - [Grünbaumian] ``` ```x3/2x5/4o5/2o3*a5/3*c - [Grünbaumian] x3/2o5/4x5/2o3*a5/3*c - affixthi x3/2o5/4o5/2x3*a5/3*c - (contains gacid) o3/2x5/4x5/2o3*a5/3*c - [Grünbaumian] o3/2x5/4o5/2x3*a5/3*c - o3/2o5/4x5/2x3*a5/3*c - [Grünbaumian] x3/2x5/4x5/2o3*a5/3*c - [Grünbaumian] x3/2x5/4o5/2x3*a5/3*c - [Grünbaumian] x3/2o5/4x5/2x3*a5/3*c - [Grünbaumian] o3/2x5/4x5/2x3*a5/3*c - [Grünbaumian] x3/2x5/4x5/2x3*a5/3*c - [Grünbaumian] ``` ```x3x5/4o5/2o3/2*a5/2*c - (contains gacid) x3o5/4x5/2o3/2*a5/2*c - [Grünbaumian] x3o5/4o5/2x3/2*a5/2*c - [Grünbaumian] o3x5/4x5/2o3/2*a5/2*c - [Grünbaumian] o3x5/4o5/2x3/2*a5/2*c - o3o5/4x5/2x3/2*a5/2*c - [Grünbaumian] x3x5/4x5/2o3/2*a5/2*c - [Grünbaumian] x3x5/4o5/2x3/2*a5/2*c - [Grünbaumian] x3o5/4x5/2x3/2*a5/2*c - [Grünbaumian] o3x5/4x5/2x3/2*a5/2*c - [Grünbaumian] x3x5/4x5/2x3/2*a5/2*c - [Grünbaumian] ``` ```x3/2x5/4o5/3o3/2*a5/3*c - [Grünbaumian] x3/2o5/4x5/3o3/2*a5/3*c - affixthi x3/2o5/4o5/3x3/2*a5/3*c - [Grünbaumian] o3/2x5/4x5/3o3/2*a5/3*c - [Grünbaumian] o3/2x5/4o5/3x3/2*a5/3*c - o3/2o5/4x5/3x3/2*a5/3*c - gefradit thix x3/2x5/4x5/3o3/2*a5/3*c - [Grünbaumian] x3/2x5/4o5/3x3/2*a5/3*c - [Grünbaumian] x3/2o5/4x5/3x3/2*a5/3*c - [Grünbaumian] o3/2x5/4x5/3x3/2*a5/3*c - [Grünbaumian] x3/2x5/4x5/3x3/2*a5/3*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5o3o5*a5/4*c   (up)

 o3o5o3o5*a5/4*c (µ=22) o3o5/4o3/2o5*a5*c (µ=98) o3/2o5o3/2o5*a5*c (µ=142) quasiregulars ```x3o5o3o5*a5/4*c - (contains "2doe") o3x5o3o5*a5/4*c - (contains cid) ``` ```x3o5/4o3/2o5*a5*c - (contains "2doe") o3x5/4o3/2o5*a5*c - (contains cid) o3o5/4x3/2o5*a5*c - (contains "2doe") o3o5/4o3/2x5*a5*c - (contains cid) ``` ```x3/2o5o3/2o5*a5*c - (contains "2doe") o3/2x5o3/2o5*a5*c - (contains cid) ``` otherWythoffians ```x3x5o3o5*a5/4*c - (contains "2doe") x3o5x3o5*a5/4*c - [Grünbaumian] x3o5o3x5*a5/4*c - (contains cid) o3x5o3x5*a5/4*c - x3x5x3o5*a5/4*c - [Grünbaumian] x3x5o3x5*a5/4*c - x3x5x3x5*a5/4*c - [Grünbaumian] ``` ```x3x5/4o3/2o5*a5*c - (contains "2doe") x3o5/4x3/2o5*a5*c - 2sadtifady (?) x3o5/4o3/2x5*a5*c - (contains cid) o3x5/4x3/2o5*a5*c - [Grünbaumian] o3x5/4o3/2x5*a5*c - o3o5/4x3/2x5*a5*c - [Grünbaumian] x3x5/4x3/2o5*a5*c - [Grünbaumian] x3x5/4o3/2x5*a5*c - x3o5/4x3/2x5*a5*c - [Grünbaumian] o3x5/4x3/2x5*a5*c - [Grünbaumian] x3x5/4x3/2x5*a5*c - [Grünbaumian] ``` ```x3/2x5o3/2o5*a5*c - [Grünbaumian] x3/2o5x3/2o5*a5*c - 2sadtifady (?) x3/2o5o3/2x5*a5*c - (contains cid) o3/2x5o3/2x5*a5*c - x3/2x5x3/2o5*a5*c - [Grünbaumian] x3/2x5o3/2x5*a5*c - [Grünbaumian] x3/2x5x3/2x5*a5*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o5/4o3o5/4*a5*c (µ=1102) o3o5o3/2o5/4*a5/4*c (µ=1178) o3/2o5/4o3/2o5/4*a5/4*c (µ=3382) quasiregulars ```x3o5/4o3o5/4*a5*c - (contains "2doe") o3x5/4o3o5/4*a5*c - (contains cid) ``` ```x3o5o3/2o5/4*a5/4*c - (contains "2doe") o3x5o3/2o5/4*a5/4*c - (contains cid) o3o5x3/2o5/4*a5/4*c - (contains "2doe") o3o5o3/2x5/4*a5/4*c - (contains cid) ``` ```x3/2o5/4o3/2o5/4*a5/4*c - (contains "2doe") o3/2x5/4o3/2o5/4*a5/4*c - (contains cid) ``` otherWythoffians ```x3x5/4o3o5/4*a5*c - (contains "2doe") x3o5/4x3o5/4*a5*c - 2sadtifady (?) x3o5/4o3x5/4*a5*c - [Grünbaumian] o3x5/4o3x5/4*a5*c - x3x5/4x3o5/4*a5*c - [Grünbaumian] x3x5/4o3x5/4*a5*c - [Grünbaumian] x3x5/4x3x5/4*a5*c - [Grünbaumian] ``` ```x3x5o3/2o5/4*a5/4*c - (contains "2doe") x3o5x3/2o5/4*a5/4*c - [Grünbaumian] x3o5o3/2x5/4*a5/4*c - [Grünbaumian] o3x5x3/2o5/4*a5/4*c - (contains cid) o3x5o3/2x5/4*a5/4*c - o3o5x3/2x5/4*a5/4*c - [Grünbaumian] x3x5x3/2o5/4*a5/4*c - [Grünbaumian] x3x5o3/2x5/4*a5/4*c - [Grünbaumian] x3o5x3/2x5/4*a5/4*c - [Grünbaumian] o3x5x3/2x5/4*a5/4*c - [Grünbaumian] x3x5x3/2x5/4*a5/4*c - [Grünbaumian] ``` ```x3/2x5/4o3/2o5/4*a5/4*c - [Grünbaumian] x3/2o5/4x3/2o5/4*a5/4*c - [Grünbaumian] x3/2o5/4o3/2x5/4*a5/4*c - [Grünbaumian] o3/2x5/4o3/2x5/4*a5/4*c - x3/2x5/4x3/2o5/4*a5/4*c - [Grünbaumian] x3/2x5/4o3/2x5/4*a5/4*c - [Grünbaumian] x3/2x5/4x3/2x5/4*a5/4*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5/2o3o5/2*a5/3*c   (up)

 o3o5/2o3o5/2*a5/3*c (µ=238) o3o5/3o3o5/3*a5/2*c (µ=598) o3o5/3o3/2o5/2*a5/2*c (µ=602) quasiregulars ```x3o5/2o3o5/2*a5/3*c - (contains "2gissid") o3x5/2o3o5/2*a5/3*c - (contains gacid) ``` ```x3o5/3o3o5/3*a5/2*c - (contains "2gissid") o3x5/3o3o5/3*a5/2*c - (contains gacid) ``` ```x3o5/3o3/2o5/2*a5/2*c - (contains "2gissid") o3x5/3o3/2o5/2*a5/2*c - (contains gacid) o3o5/3x3/2o5/2*a5/2*c - (contains "2gissid") o3o5/3o3/2x5/2*a5/2*c - (contains gacid) ``` otherWythoffians ```x3x5/2o3o5/2*a5/3*c - (contains "2gissid") x3o5/2x3o5/2*a5/3*c - 2gadtifady (?) x3o5/2o3x5/2*a5/3*c - [Grünbaumian] o3x5/2o3x5/2*a5/3*c - x3x5/2x3o5/2*a5/3*c - [Grünbaumian] x3x5/2o3x5/2*a5/3*c - [Grünbaumian] x3x5/2x3x5/2*a5/3*c - [Grünbaumian] ``` ```x3x5/3o3o5/3*a5/2*c - (contains "2gissid") x3o5/3x3o5/3*a5/2*c - [Grünbaumian] x3o5/3o3x5/3*a5/2*c - (contains gacid) o3x5/3o3x5/3*a5/2*c - x3x5/3x3o5/3*a5/2*c - [Grünbaumian] x3x5/3o3x5/3*a5/2*c - x3x5/3x3x5/3*a5/2*c - [Grünbaumian] ``` ```x3x5/3o3/2o5/2*a5/2*c - (contains "2gissid") x3o5/3x3/2o5/2*a5/2*c - [Grünbaumian] x3o5/3o3/2x5/2*a5/2*c - [Grünbaumian] o3x5/3x3/2o5/2*a5/2*c - (contains gacid) o3x5/3o3/2x5/2*a5/2*c - o3o5/3x3/2x5/2*a5/2*c - [Grünbaumian] x3x5/3x3/2o5/2*a5/2*c - [Grünbaumian] x3x5/3o3/2x5/2*a5/2*c - [Grünbaumian] x3o5/3x3/2x5/2*a5/2*c - [Grünbaumian] o3x5/3x3/2x5/2*a5/2*c - [Grünbaumian] x3x5/3x3/2x5/2*a5/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o5/2o3/2o5/3*a5/3*c (µ=962) o3/2o5/2o3/2o5/2*a5/2*c (µ=1078) o3/2o5/3o3/2o5/3*a5/3*c (µ=2158) quasiregulars ```x3o5/2o3/2o5/3*a5/3*c - (contains "2gissid") o3x5/2o3/2o5/3*a5/3*c - (contains gacid) o3o5/2x3/2o5/3*a5/3*c - (contains "2gissid") o3o5/2o3/2x5/3*a5/3*c - (contains gacid) ``` ```x3/2o5/2o3/2o5/2*a5/2*c - (contains "2gissid") o3/2x5/2o3/2o5/2*a5/2*c - (contains gacid) ``` ```x3/2o5/3o3/2o5/3*a5/3*c - (contains "2gissid") o3/2x5/3o3/2o5/3*a5/3*c - (contains gacid) ``` otherWythoffians ```x3x5/2o3/2o5/3*a5/3*c - (contains "2gissid") x3o5/2x3/2o5/3*a5/3*c - 2gadtifady (?) x3o5/2o3/2x5/3*a5/3*c - (contains gacid) o3x5/2x3/2o5/3*a5/3*c - [Grünbaumian] o3x5/2o3/2x5/3*a5/3*c - o3o5/2x3/2x5/3*a5/3*c - [Grünbaumian] x3x5/2x3/2o5/3*a5/3*c - [Grünbaumian] x3x5/2o3/2x5/3*a5/3*c - x3o5/2x3/2x5/3*a5/3*c - [Grünbaumian] o3x5/2x3/2x5/3*a5/3*c - [Grünbaumian] x3x5/2x3/2x5/3*a5/3*c - [Grünbaumian] ``` ```x3/2x5/2o3/2o5/2*a5/2*c - [Grünbaumian] x3/2o5/2x3/2o5/2*a5/2*c - [Grünbaumian] x3/2o5/2o3/2x5/2*a5/2*c - [Grünbaumian] o3/2x5/2o3/2x5/2*a5/2*c - x3/2x5/2x3/2o5/2*a5/2*c - [Grünbaumian] x3/2x5/2o3/2x5/2*a5/2*c - [Grünbaumian] x3/2x5/2x3/2x5/2*a5/2*c - [Grünbaumian] ``` ```x3/2x5/3o3/2o5/3*a5/3*c - [Grünbaumian] x3/2o5/3x3/2o5/3*a5/3*c - 2gadtifady (?) x3/2o5/3o3/2x5/3*a5/3*c - (contains gacid) o3/2x5/3o3/2x5/3*a5/3*c - x3/2x5/3x3/2o5/3*a5/3*c - [Grünbaumian] x3/2x5/3o3/2x5/3*a5/3*c - [Grünbaumian] x3/2x5/3x3/2x5/3*a5/3*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5/2o5o5*a5/4*c   (up)

 o3o5/2o5o5*a5/4*c (µ=38) o3o5/3o5/4o5*a5*c (µ=82) o3/2o5/2o5o5/4*a5*c (µ=322) o3o5/3o5o5/4*a5*c (µ=398) quasiregulars ```x3o5/2o5o5*a5/4*c - (contains "2gad") o3x5/2o5o5*a5/4*c - (contains gacid) o3o5/2x5o5*a5/4*c - (contains "2gad") o3o5/2o5x5*a5/4*c - (contains "2gad") ``` ```x3o5/3o5/4o5*a5*c - (contains "2gad") o3x5/3o5/4o5*a5*c - (contains gacid) o3o5/3x5/4o5*a5*c - (contains "2gad") o3o5/3o5/4x5*a5*c - (contains "2gad") ``` ```x3/2o5/2o5o5/4*a5*c - (contains "2gad") o3/2x5/2o5o5/4*a5*c - (contains gacid) o3/2o5/2x5o5/4*a5*c - (contains "2gad") o3/2o5/2o5x5/4*a5*c - (contains "2gad") ``` ```x3o5/3o5o5/4*a5*c - (contains "2gad") o3x5/3o5o5/4*a5*c - (contains gacid) o3o5/3x5o5/4*a5*c - (contains "2gad") o3o5/3o5x5/4*a5*c - (contains "2gad") ``` otherWythoffians ```x3x5/2o5o5*a5/4*c - (contains "2gad") x3o5/2x5o5*a5/4*c - [Grünbaumian] x3o5/2o5x5*a5/4*c - (contains gacid) o3x5/2x5o5*a5/4*c - [Grünbaumian] o3x5/2o5x5*a5/4*c - o3o5/2x5x5*a5/4*c - (contains "2sidhid") x3x5/2x5o5*a5/4*c - [Grünbaumian] x3x5/2o5x5*a5/4*c - x3o5/2x5x5*a5/4*c - [Grünbaumian] o3x5/2x5x5*a5/4*c - [Grünbaumian] x3x5/2x5x5*a5/4*c - [Grünbaumian] ``` ```x3x5/3o5/4o5*a5*c - (contains "2gad") x3o5/3x5/4o5*a5*c - (contains "2sidhid") x3o5/3o5/4x5*a5*c - (contains gacid) o3x5/3x5/4o5*a5*c - (contains "2gad") o3x5/3o5/4x5*a5*c - o3o5/3x5/4x5*a5*c - [Grünbaumian] x3x5/3x5/4o5*a5*c - (contains "2sidhid") x3x5/3o5/4x5*a5*c - x3o5/3x5/4x5*a5*c - [Grünbaumian] o3x5/3x5/4x5*a5*c - [Grünbaumian] x3x5/3x5/4x5*a5*c - [Grünbaumian] ``` ```x3/2x5/2o5o5/4*a5*c - [Grünbaumian] x3/2o5/2x5o5/4*a5*c - (contains "2sidhid") x3/2o5/2o5x5/4*a5*c - [Grünbaumian] o3/2x5/2x5o5/4*a5*c - [Grünbaumian] o3/2x5/2o5x5/4*a5*c - o3/2o5/2x5x5/4*a5*c - (contains "2sidhid") x3/2x5/2x5o5/4*a5*c - [Grünbaumian] x3/2x5/2o5x5/4*a5*c - [Grünbaumian] x3/2o5/2x5x5/4*a5*c - [Grünbaumian] o3/2x5/2x5x5/4*a5*c - [Grünbaumian] x3/2x5/2x5x5/4*a5*c - [Grünbaumian] ``` ```x3x5/3o5o5/4*a5*c - (contains "2gad") x3o5/3x5o5/4*a5*c - (contains "2sidhid") x3o5/3o5x5/4*a5*c - [Grünbaumian] o3x5/3x5o5/4*a5*c - (contains "2gad") o3x5/3o5x5/4*a5*c - o3o5/3x5x5/4*a5*c - (contains "2sidhid") x3x5/3x5o5/4*a5*c - (contains "2sidhid") x3x5/3o5x5/4*a5*c - [Grünbaumian] x3o5/3x5x5/4*a5*c - [Grünbaumian] o3x5/3x5x5/4*a5*c - x3x5/3x5x5/4*a5*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o5/2o5/4o5*a5*c (µ=638) o3/2o5/3o5o5*a5/4*c (µ=682) o3o5/2o5/4o5/4*a5/4*c (µ=1882) o3/2o5/3o5/4o5/4*a5/4*c (µ=3158) quasiregulars ```x3/2o5/2o5/4o5*a5*c - (contains "2gad") o3/2x5/2o5/4o5*a5*c - (contains gacid) o3/2o5/2x5/4o5*a5*c - (contains "2gad") o3/2o5/2o5/4x5*a5*c - (contains "2gad") ``` ```x3/2o5/3o5o5*a5/4*c - (contains "2gad") o3/2x5/3o5o5*a5/4*c - (contains gacid) o3/2o5/3x5o5*a5/4*c - (contains "2gad") o3/2o5/3o5x5*a5/4*c - (contains "2gad") ``` ```x3o5/2o5/4o5/4*a5/4*c - (contains "2gad") o3x5/2o5/4o5/4*a5/4*c - (contains gacid) o3o5/2x5/4o5/4*a5/4*c - (contains "2gad") o3o5/2o5/4x5/4*a5/4*c - (contains "2gad") ``` ```x3/2o5/3o5/4o5/4*a5/4*c - (contains "2gad") o3/2x5/3o5/4o5/4*a5/4*c - (contains gacid) o3/2o5/3x5/4o5/4*a5/4*c - (contains "2gad") o3/2o5/3o5/4x5/4*a5/4*c - (contains "2gad") ``` otherWythoffians ```x3/2x5/2o5/4o5*a5*c - [Grünbaumian] x3/2o5/2x5/4o5*a5*c - (contains "2sidhid") x3/2o5/2o5/4x5*a5*c - (contains gacid) o3/2x5/2x5/4o5*a5*c - [Grünbaumian] o3/2x5/2o5/4x5*a5*c - o3/2o5/2x5/4x5*a5*c - [Grünbaumian] x3/2x5/2x5/4o5*a5*c - [Grünbaumian] x3/2x5/2o5/4x5*a5*c - [Grünbaumian] x3/2o5/2x5/4x5*a5*c - [Grünbaumian] o3/2x5/2x5/4x5*a5*c - [Grünbaumian] x3/2x5/2x5/4x5*a5*c - [Grünbaumian] ``` ```x3/2x5/3o5o5*a5/4*c - [Grünbaumian] x3/2o5/3x5o5*a5/4*c - [Grünbaumian] x3/2o5/3o5x5*a5/4*c - (contains gacid) o3/2x5/3x5o5*a5/4*c - (contains "2gad") o3/2x5/3o5x5*a5/4*c - o3/2o5/3x5x5*a5/4*c - (contains "2sidhid") x3/2x5/3x5o5*a5/4*c - [Grünbaumian] x3/2x5/3o5x5*a5/4*c - [Grünbaumian] x3/2o5/3x5x5*a5/4*c - [Grünbaumian] o3/2x5/3x5x5*a5/4*c - x3/2x5/3x5x5*a5/4*c - [Grünbaumian] ``` ```x3x5/2o5/4o5/4*a5/4*c - (contains "2gad") x3o5/2x5/4o5/4*a5/4*c - [Grünbaumian] x3o5/2o5/4x5/4*a5/4*c - [Grünbaumian] o3x5/2x5/4o5/4*a5/4*c - [Grünbaumian] o3x5/2o5/4x5/4*a5/4*c - o3o5/2x5/4x5/4*a5/4*c - [Grünbaumian] x3x5/2x5/4o5/4*a5/4*c - [Grünbaumian] x3x5/2o5/4x5/4*a5/4*c - [Grünbaumian] x3o5/2x5/4x5/4*a5/4*c - [Grünbaumian] o3x5/2x5/4x5/4*a5/4*c - [Grünbaumian] x3x5/2x5/4x5/4*a5/4*c - [Grünbaumian] ``` ```x3/2x5/3o5/4o5/4*a5/4*c - [Grünbaumian] x3/2o5/3x5/4o5/4*a5/4*c - [Grünbaumian] x3/2o5/3o5/4x5/4*a5/4*c - [Grünbaumian] o3/2x5/3x5/4o5/4*a5/4*c - (contains "2gad") o3/2x5/3o5/4x5/4*a5/4*c - o3/2o5/3x5/4x5/4*a5/4*c - [Grünbaumian] x3/2x5/3x5/4o5/4*a5/4*c - [Grünbaumian] x3/2x5/3o5/4x5/4*a5/4*c - [Grünbaumian] x3/2o5/3x5/4x5/4*a5/4*c - [Grünbaumian] o3/2x5/3x5/4x5/4*a5/4*c - [Grünbaumian] x3/2x5/3x5/4x5/4*a5/4*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3/2o5o5/2o5/2*a5/2*c   (up)

 o3/2o5o5/2o5/2*a5/2*c (µ=178) o3o5o5/2o5/3*a5/3*c (µ=182) o3o5o5/3o5/2*a5/3*c (µ=298) o3o5/4o5/2o5/2*a5/2*c (µ=542) quasiregulars ```x3/2o5o5/2o5/2*a5/2*c - (contains "2sissid") o3/2x5o5/2o5/2*a5/2*c - (contains cid) o3/2o5x5/2o5/2*a5/2*c - (contains "2sissid") o3/2o5o5/2x5/2*a5/2*c - (contains "2sissid") ``` ```x3o5o5/2o5/3*a5/3*c - (contains "2sissid") o3x5o5/2o5/3*a5/3*c - (contains cid) o3o5x5/2o5/3*a5/3*c - (contains "2sissid") o3o5o5/2x5/3*a5/3*c - (contains "2sissid") ``` ```x3o5o5/3o5/2*a5/3*c - (contains "2sissid") o3x5o5/3o5/2*a5/3*c - (contains cid) o3o5x5/3o5/2*a5/3*c - (contains "2sissid") o3o5o5/3x5/2*a5/3*c - (contains "2sissid") ``` ```x3o5/4o5/2o5/2*a5/2*c - (contains "2sissid") o3x5/4o5/2o5/2*a5/2*c - (contains cid) o3o5/4x5/2o5/2*a5/2*c - (contains "2sissid") o3o5/4o5/2x5/2*a5/2*c - (contains "2sissid") ``` otherWythoffians ```x3/2x5o5/2o5/2*a5/2*c - [Grünbaumian] x3/2o5x5/2o5/2*a5/2*c - [Grünbaumian] x3/2o5o5/2x5/2*a5/2*c - [Grünbaumian] o3/2x5x5/2o5/2*a5/2*c - (contains "2sissid") o3/2x5o5/2x5/2*a5/2*c - o3/2o5x5/2x5/2*a5/2*c - [Grünbaumian] x3/2x5x5/2o5/2*a5/2*c - [Grünbaumian] x3/2x5o5/2x5/2*a5/2*c - [Grünbaumian] x3/2o5x5/2x5/2*a5/2*c - [Grünbaumian] o3/2x5x5/2x5/2*a5/2*c - [Grünbaumian] x3/2x5x5/2x5/2*a5/2*c - [Grünbaumian] ``` ```x3x5o5/2o5/3*a5/3*c - (contains "2sissid") x3o5x5/2o5/3*a5/3*c - (contains "2gidhid") x3o5o5/2x5/3*a5/3*c - (contains "2gidhid") o3x5x5/2o5/3*a5/3*c - (contains "2sissid") o3x5o5/2x5/3*a5/3*c - o3o5x5/2x5/3*a5/3*c - [Grünbaumian] x3x5x5/2o5/3*a5/3*c - (contains "2gidhid") x3x5o5/2x5/3*a5/3*c - x3o5x5/2x5/3*a5/3*c - [Grünbaumian] o3x5x5/2x5/3*a5/3*c - [Grünbaumian] x3x5x5/2x5/3*a5/3*c - [Grünbaumian] ``` ```x3x5o5/3o5/2*a5/3*c - (contains "2sissid") x3o5x5/3o5/2*a5/3*c - (contains "2gidhid") x3o5o5/3x5/2*a5/3*c - [Grünbaumian] o3x5x5/3o5/2*a5/3*c - (contains "2sissid") o3x5o5/3x5/2*a5/3*c - o3o5x5/3x5/2*a5/3*c - (contains "2gidhid") x3x5x5/3o5/2*a5/3*c - (contains "2gidhid") x3x5o5/3x5/2*a5/3*c - [Grünbaumian] x3o5x5/3x5/2*a5/3*c - [Grünbaumian] o3x5x5/3x5/2*a5/3*c - x3x5x5/3x5/2*a5/3*c - [Grünbaumian] ``` ```x3x5/4o5/2o5/2*a5/2*c - (contains "2sissid") x3o5/4x5/2o5/2*a5/2*c - [Grünbaumian] x3o5/4o5/2x5/2*a5/2*c - [Grünbaumian] o3x5/4x5/2o5/2*a5/2*c - [Grünbaumian] o3x5/4o5/2x5/2*a5/2*c - o3o5/4x5/2x5/2*a5/2*c - [Grünbaumian] x3x5/4x5/2o5/2*a5/2*c - [Grünbaumian] x3x5/4o5/2x5/2*a5/2*c - [Grünbaumian] x3o5/4x5/2x5/2*a5/2*c - [Grünbaumian] o3x5/4x5/2x5/2*a5/2*c - [Grünbaumian] x3x5/4x5/2x5/2*a5/2*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o5o5/3o5/3*a5/2*c (µ=782) o3o5/4o5/3o5/3*a5/2*c (µ=1378) o3/2o5/4o5/3o5/2*a5/3*c (µ=1862) o3/2o5/4o5/2o5/3*a5/3*c (µ=1978) quasiregulars ```x3/2o5o5/3o5/3*a5/2*c - (contains "2sissid") o3/2x5o5/3o5/3*a5/2*c - (contains cid) o3/2o5x5/3o5/3*a5/2*c - (contains "2sissid") o3/2o5o5/3x5/3*a5/2*c - (contains "2sissid") ``` ```x3o5/4o5/3o5/3*a5/2*c - (contains "2sissid") o3x5/4o5/3o5/3*a5/2*c - (contains cid) o3o5/4x5/3o5/3*a5/2*c - (contains "2sissid") o3o5/4o5/3x5/3*a5/2*c - (contains "2sissid") ``` ```x3/2o5/4o5/3o5/2*a5/3*c - (contains "2sissid") o3/2x5/4o5/3o5/2*a5/3*c - (contains cid) o3/2o5/4x5/3o5/2*a5/3*c - (contains "2sissid") o3/2o5/4o5/3x5/2*a5/3*c - (contains "2sissid") ``` ```x3/2o5/4o5/2o5/3*a5/3*c - (contains "2sissid") o3/2x5/4o5/2o5/3*a5/3*c - (contains cid) o3/2o5/4x5/2o5/3*a5/3*c - (contains "2sissid") o3/2o5/4o5/2x5/3*a5/3*c - (contains "2sissid") ``` otherWythoffians ```x3/2x5o5/3o5/3*a5/2*c - [Grünbaumian] x3/2o5x5/3o5/3*a5/2*c - [Grünbaumian] x3/2o5o5/3x5/3*a5/2*c - (contains "2gidhid") o3/2x5x5/3o5/3*a5/2*c - (contains "2sissid") o3/2x5o5/3x5/3*a5/2*c - o3/2o5x5/3x5/3*a5/2*c - (contains "2gidhid") x3/2x5x5/3o5/3*a5/2*c - [Grünbaumian] x3/2x5o5/3x5/3*a5/2*c - [Grünbaumian] x3/2o5x5/3x5/3*a5/2*c - [Grünbaumian] o3/2x5x5/3x5/3*a5/2*c - x3/2x5x5/3x5/3*a5/2*c - [Grünbaumian] ``` ```x3x5/4o5/3o5/3*a5/2*c - (contains "2sissid") x3o5/4x5/3o5/3*a5/2*c - [Grünbaumian] x3o5/4o5/3x5/3*a5/2*c - (contains "2gidhid") o3x5/4x5/3o5/3*a5/2*c - [Grünbaumian] o3x5/4o5/3x5/3*a5/2*c - o3o5/4x5/3x5/3*a5/2*c - (contains "2gidhid") x3x5/4x5/3o5/3*a5/2*c - [Grünbaumian] x3x5/4o5/3x5/3*a5/2*c - x3o5/4x5/3x5/3*a5/2*c - [Grünbaumian] o3x5/4x5/3x5/3*a5/2*c - [Grünbaumian] x3x5/4x5/3x5/3*a5/2*c - [Grünbaumian] ``` ```x3/2x5/4o5/3o5/2*a5/3*c - [Grünbaumian] x3/2o5/4x5/3o5/2*a5/3*c - (contains "2gidhid") x3/2o5/4o5/3x5/2*a5/3*c - [Grünbaumian] o3/2x5/4x5/3o5/2*a5/3*c - [Grünbaumian] o3/2x5/4o5/3x5/2*a5/3*c - o3/2o5/4x5/3x5/2*a5/3*c - (contains "2gidhid") x3/2x5/4x5/3o5/2*a5/3*c - [Grünbaumian] x3/2x5/4o5/3x5/2*a5/3*c - [Grünbaumian] x3/2o5/4x5/3x5/2*a5/3*c - [Grünbaumian] o3/2x5/4x5/3x5/2*a5/3*c - [Grünbaumian] x3/2x5/4x5/3x5/2*a5/3*c - [Grünbaumian] ``` ```x3/2x5/4o5/2o5/3*a5/3*c - [Grünbaumian] x3/2o5/4x5/2o5/3*a5/3*c - (contains "2gidhid") x3/2o5/4o5/2x5/3*a5/3*c - (contains "2gidhid") o3/2x5/4x5/2o5/3*a5/3*c - [Grünbaumian] o3/2x5/4o5/2x5/3*a5/3*c - o3/2o5/4x5/2x5/3*a5/3*c - [Grünbaumian] x3/2x5/4x5/2o5/3*a5/3*c - [Grünbaumian] x3/2x5/4o5/2x5/3*a5/3*c - [Grünbaumian] x3/2o5/4x5/2x5/3*a5/3*c - [Grünbaumian] o3/2x5/4x5/2x5/3*a5/3*c - [Grünbaumian] x3/2x5/4x5/2x5/3*a5/3*c - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

 simplical ones ```o-P-o-Q-o-R-o-S-*a-T-*c *b-U-*d = o / T \ P _o_ S /_Q R_\ o-----U-----o ```

### Pentachoral ("pentic") Symmetries   (up)

 o3o3o3o3*a3/2*c *b3/2*d (µ=6) o3/2o3/2o3/2o3/2*a3/2*c *b3/2*d (µ=24) quasiregulars ```x3o3o3o3*a3/2*c *b3/2*d - (contains "2tet") ``` ```x3/2o3/2o3/2o3/2*a3/2*c *b3/2*d - (contains "2tet") ``` otherWythoffians ```x3x3o3o3*a3/2*c *b3/2*d - x3o3x3o3*a3/2*c *b3/2*d - [Grünbaumian] x3x3x3o3*a3/2*c *b3/2*d - [Grünbaumian] x3x3x3x3*a3/2*c *b3/2*d - [Grünbaumian] ``` ```x3/2x3/2o3/2o3/2*a3/2*c *b3/2*d - [Grünbaumian] x3/2x3/2x3/2o3/2*a3/2*c *b3/2*d - [Grünbaumian] x3/2x3/2x3/2x3/2*a3/2*c *b3/2*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ```

### Tesseractic ("tessic") Symmetries   (up)

 o3/2o3/2o4o4*a3/2*c *b4*d (µ=6) o3o3o4o4*a3/2*c *b4/3*d (µ=10) quasiregulars ```x3/2o3/2o4o4*a3/2*c *b4*d - (contains "2tet","oct+6{4}") o3/2o3/2o4x4*a3/2*c *b4*d - 6tes (?) ``` ```x3o3o4o4*a3/2*c *b4/3*d - (contains "2tet","oct+6{4}") o3x3o4o4*a3/2*c *b4/3*d - (contains "2tet","oct+6{4}") o3o3o4x4*a3/2*c *b4/3*d - 6tes (?) ``` otherWythoffians ```x3/2x3/2o4o4*a3/2*c *b4*d - [Grünbaumian] x3/2o3/2o4x4*a3/2*c *b4*d - x3/2x3/2x4o4*a3/2*c *b4*d - [Grünbaumian] x3/2x3/2o4x4*a3/2*c *b4*d - [Grünbaumian] x3/2x3/2x4x4*a3/2*c *b4*d - [Grünbaumian] ``` ```x3x3o4o4*a3/2*c *b4/3*d - x3o3x4o4*a3/2*c *b4/3*d - [Grünbaumian] x3o3o4x4*a3/2*c *b4/3*d - o3x3o4x4*a3/2*c *b4/3*d - x3x3x4o4*a3/2*c *b4/3*d - [Grünbaumian] x3x3o4x4*a3/2*c *b4/3*d - kavahto x3o3x4x4*a3/2*c *b4/3*d - [Grünbaumian] x3x3x4x4*a3/2*c *b4/3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` o3o3o4/3o4/3*a3/2*c *b4*d (µ=22) o3/2o3/2o4/3o4/3*a3/2*c *b4/3*d (µ=90) quasiregulars ```x3o3o4/3o4/3*a3/2*c *b4*d - (contains "2tet","oct+6{4}") o3x3o4/3o4/3*a3/2*c *b4*d - (contains "2tet","oct+6{4}") o3o3o4/3x4/3*a3/2*c *b4*d - 6tes (?) ``` ```x3/2o3/2o4/3o4/3*a3/2*c *b4/3*d - (contains "2tet","oct+6{4}") o3/2o3/2o4/3x4/3*a3/2*c *b4/3*d - 6tes (?) ``` otherWythoffians ```x3x3o4/3o4/3*a3/2*c *b4*d - x3o3x4/3o4/3*a3/2*c *b4*d - [Grünbaumian] x3o3o4/3x4/3*a3/2*c *b4*d - o3x3o4/3x4/3*a3/2*c *b4*d - x3x3x4/3o4/3*a3/2*c *b4*d - [Grünbaumian] x3x3o4/3x4/3*a3/2*c *b4*d - x3o3x4/3x4/3*a3/2*c *b4*d - [Grünbaumian] x3x3x4/3x4/3*a3/2*c *b4*d - [Grünbaumian] ``` ```x3/2x3/2o4/3o4/3*a3/2*c *b4/3*d - [Grünbaumian] x3/2o3/2o4/3x4/3*a3/2*c *b4/3*d - x3/2x3/2x4/3o4/3*a3/2*c *b4/3*d - [Grünbaumian] x3/2x3/2o4/3x4/3*a3/2*c *b4/3*d - [Grünbaumian] x3/2x3/2x4/3x4/3*a3/2*c *b4/3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ```

### Icositetrachoral ("icoic") Symmetries   (up)

 o4o4o4o4*a3/2*c *b3/2*d (µ=4) o3o4o3/2o4/3*a4/3*c *b4*d (µ=44) quasiregulars ```x4o4o4o4*a3/2*c *b3/2*d - 2ico+2gico (?) ``` ```x3o4o3/2o4/3*a4/3*c *b4*d - 2ico+2gico (?) o3x4o3/2o4/3*a4/3*c *b4*d - 2ico+2gico (?) o3o4x3/2o4/3*a4/3*c *b4*d - 2ico+2gico (?) ``` otherWythoffians ```x4x4o4o4*a3/2*c *b3/2*d - x4o4x4o4*a3/2*c *b3/2*d - [Grünbaumian] x4x4x4o4*a3/2*c *b3/2*d - [Grünbaumian] x4x4x4x4*a3/2*c *b3/2*d - [Grünbaumian] ``` ```x3x4o3/2o4/3*a4/3*c *b4*d - x3o4x3/2o4/3*a4/3*c *b4*d - o3x4x3/2o4/3*a4/3*c *b4*d - o3o4x3/2x4/3*a4/3*c *b4*d - [Grünbaumian] x3x4x3/2o4/3*a4/3*c *b4*d - x3o4x3/2x4/3*a4/3*c *b4*d - [Grünbaumian] o3x4x3/2x4/3*a4/3*c *b4*d - [Grünbaumian] x3x4x3/2x4/3*a4/3*c *b4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` o3o4o3o4*a4/3*c *c4/3*d (µ=52) o3/2o4/3o3/2o4/3*a4/3*c *b4/3*d (µ=292) quasiregulars ```x3o4o3o4*a4/3*c *b4/3*d - 2ico+2gico (?) ``` ```x3/2o4/3o3/2o4/3*a4/3*c *b4/3*d - 2ico+2gico (?) ``` otherWythoffians ```x3x4o3o4*a4/3*c *b4/3*d - x3o4x3o4*a4/3*c *b4/3*d - x3o4o3x4*a4/3*c *b4/3*d - x3x4x3o4*a4/3*c *b4/3*d - x3x4x3x4*a4/3*c *b4/3*d - 2affic (?) ``` ```x3/2x4/3o3/2o4/3*a4/3*c *b4/3*d - [Grünbaumian] x3/2o4/3x3/2o4/3*a4/3*c *b4/3*d - x3/2x4/3x3/2o4/3*a4/3*c *b4/3*d - [Grünbaumian] x3/2x4/3x3/2x4/3*a4/3*c *b4/3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3/2o3o3/2*a3*c *b5*d   (up)

 o3o3/2o3o3/2*a3*c *b5*d (µ=284) o3o3o3/2o3/2*a3/2*c *b5*d (µ=436) o3o3o3o3*a3/2*c *b5/4*d (µ=764) quasiregulars ```x3o3/2o3o3/2*a3*c *b5*d - (contains "2tet") o3x3/2o3o3/2*a3*c *b5*d - (contains "2tet") ``` ```x3o3o3/2o3/2*a3/2*c *b5*d - (contains "2tet") o3x3o3/2o3/2*a3/2*c *b5*d - (contains "2tet") o3o3o3/2x3/2*a3/2*c *b5*d - (contains "2tet") ``` ```x3o3o3o3*a3/2*c *b5/4*d - (contains "2tet") o3x3o3o3*a3/2*c *b5/4*d - (contains "2tet") ``` otherWythoffians ```x3x3/2o3o3/2*a3*c *b5*d - x3o3/2x3o3/2*a3*c *b5*d - x3o3/2o3x3/2*a3*c *b5*d - [Grünbaumian] o3x3/2o3x3/2*a3*c *b5*d - x3x3/2x3o3/2*a3*c *b5*d - [Grünbaumian] x3x3/2o3x3/2*a3*c *b5*d - [Grünbaumian] x3x3/2x3x3/2*a3*c *b5*d - [Grünbaumian] ``` ```x3x3o3/2o3/2*a3/2*c *b5*d - x3o3x3/2o3/2*a3/2*c *b5*d - [Grünbaumian] x3o3o3/2x3/2*a3/2*c *b5*d - [Grünbaumian] o3x3o3/2x3/2*a3/2*c *b5*d - x3x3x3/2o3/2*a3/2*c *b5*d - [Grünbaumian] x3x3o3/2x3/2*a3/2*c *b5*d - [Grünbaumian] x3o3x3/2x3/2*a3/2*c *b5*d - [Grünbaumian] x3x3x3/2x3/2*a3/2*c *b5*d - [Grünbaumian] ``` ```x3x3o3o3*a3/2*c *b5/4*d - x3o3x3o3*a3/2*c *b5/4*d - [Grünbaumian] o3x3o3x3*a3/2*c *b5/4*d - [Grünbaumian] x3x3x3o3*a3/2*c *b5/4*d - [Grünbaumian] x3x3o3x3*a3/2*c *b5/4*d - [Grünbaumian] x3x3x3x3*a3/2*c *b5/4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o3/2o3/2o3*a3*c *b5/4*d (µ=916) o3/2o3/2o3/2o3/2*a3/2*c *b5/4*d (µ=3164) quasiregulars ```x3o3/2o3/2o3*a3*c *b5/4*d - (contains "2tet") o3x3/2o3/2o3*a3*c *b5/4*d - (contains "2tet") o3o3/2x3/2o3*a3*c *b5/4*d - (contains "2tet") ``` ```x3/2o3/2o3/2o3/2*a3/2*c *b5/4*d - (contains "2tet") o3/2x3/2o3/2o3/2*a3/2*c *b5/4*d - (contains "2tet") ``` otherWythoffians ```x3x3/2o3/2o3*a3*c *b5/4*d - x3o3/2x3/2o3*a3*c *b5/4*d - o3x3/2x3/2o3*a3*c *b5/4*d - [Grünbaumian] o3x3/2o3/2x3*a3*c *b5/4*d - [Grünbaumian] x3x3/2x3/2o3*a3*c *b5/4*d - [Grünbaumian] x3x3/2o3/2x3*a3*c *b5/4*d - [Grünbaumian] o3x3/2x3/2x3*a3*c *b5/4*d - [Grünbaumian] x3x3/2x3/2x3*a3*c *b5/4*d - [Grünbaumian] ``` ```x3/2x3/2o3/2o3/2*a3/2*c *b5/4*d - [Grünbaumian] x3/2o3/2x3/2o3/2*a3/2*c *b5/4*d - [Grünbaumian] o3/2x3/2o3/2x3/2*a3/2*c *b5/4*d - [Grünbaumian] x3/2x3/2x3/2o3/2*a3/2*c *b5/4*d - [Grünbaumian] x3/2x3/2o3/2x3/2*a3/2*c *b5/4*d - [Grünbaumian] x3/2x3/2x3/2x3/2*a3/2*c *b5/4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o3o3*a3/2*c *b5/2*d   (up)

 o3o3o3o3*a3/2*c *b5/2*d (µ=4) o3o3/2o3/2o3*a3*c *b5/2*d (µ=236) o3o3/2o3o3/2*a3*c *b5/3*d (µ=964) quasiregulars ```x3o3o3o3*a3/2*c *b5/2*d - (contains "2tet") o3x3o3o3*a3/2*c *b5/2*d - (contains "2tet") ``` ```x3o3/2o3/2o3*a3*c *b5/2*d - (contains "2tet") o3x3/2o3/2o3*a3*c *b5/2*d - (contains "2tet") o3o3/2x3/2o3*a3*c *b5/2*d - (contains "2tet") ``` ```x3o3/2o3o3/2*a3*c *b5/3*d - (contains "2tet") o3x3/2o3o3/2*a3*c *b5/3*d - (contains "2tet") ``` otherWythoffians ```x3x3o3o3*a3/2*c *b5/2*d - x3o3x3o3*a3/2*c *b5/2*d - [Grünbaumian] o3x3o3x3*a3/2*c *b5/2*d - [Grünbaumian] x3x3x3o3*a3/2*c *b5/2*d - [Grünbaumian] x3x3o3x3*a3/2*c *b5/2*d - [Grünbaumian] x3x3x3x3*a3/2*c *b5/2*d - [Grünbaumian] ``` ```x3x3/2o3/2o3*a3*c *b5/2*d - x3o3/2x3/2o3*a3*c *b5/2*d - o3x3/2x3/2o3*a3*c *b5/2*d - [Grünbaumian] o3x3/2o3/2x3*a3*c *b5/2*d - [Grünbaumian] x3x3/2x3/2o3*a3*c *b5/2*d - [Grünbaumian] x3x3/2o3/2x3*a3*c *b5/2*d - [Grünbaumian] o3x3/2x3/2x3*a3*c *b5/2*d - [Grünbaumian] x3x3/2x3/2x3*a3*c *b5/2*d - [Grünbaumian] ``` ```x3x3/2o3o3/2*a3*c *b5/3*d - x3o3/2x3o3/2*a3*c *b5/3*d - x3o3/2o3x3/2*a3*c *b5/3*d - [Grünbaumian] o3x3/2o3x3/2*a3*c *b5/3*d - x3x3/2x3o3/2*a3*c *b5/3*d - [Grünbaumian] x3x3/2o3x3/2*a3*c *b5/3*d - [Grünbaumian] x3x3/2x3x3/2*a3*c *b5/3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o3o3/2o3/2*a3/2*c *b5/3*d (µ=1196) o3/2o3/2o3/2o3/2*a3/2*c *b5/2*d (µ=2404) quasiregulars ```x3o3o3/2o3/2*a3/2*c *b5/3*d - (contains "2tet") o3x3o3/2o3/2*a3/2*c *b5/3*d - (contains "2tet") o3o3o3/2x3/2*a3/2*c *b5/3*d - (contains "2tet") ``` ```x3/2o3/2o3/2o3/2*a3/2*c *b5/2*d - (contains "2tet") o3/2x3/2o3/2o3/2*a3/2*c *b5/2*d - (contains "2tet") ``` otherWythoffians ```x3x3o3/2o3/2*a3/2*c *b5/3*d - x3o3x3/2o3/2*a3/2*c *b5/3*d - [Grünbaumian] x3o3o3/2x3/2*a3/2*c *b5/3*d - [Grünbaumian] o3x3o3/2x3/2*a3/2*c *b5/3*d - x3x3x3/2o3/2*a3/2*c *b5/3*d - [Grünbaumian] x3x3o3/2x3/2*a3/2*c *b5/3*d - [Grünbaumian] x3o3x3/2x3/2*a3/2*c *b5/3*d - [Grünbaumian] x3x3x3/2x3/2*a3/2*c *b5/3*d - [Grünbaumian] ``` ```x3/2x3/2o3/2o3/2*a3/2*c *b5/2*d - [Grünbaumian] x3/2o3/2x3/2o3/2*a3/2*c *b5/2*d - [Grünbaumian] o3/2x3/2o3/2x3/2*a3/2*c *b5/2*d - [Grünbaumian] x3/2x3/2x3/2o3/2*a3/2*c *b5/2*d - [Grünbaumian] x3/2x3/2o3/2x3/2*a3/2*c *b5/2*d - [Grünbaumian] x3/2x3/2x3/2x3/2*a3/2*c *b5/2*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3/2o3o3/2o5*a5*c *b3*d   (up)

 o3/2o3o3/2o5*a5*c *b3*d (µ=78) o3o3/2o3/2o5*a5*c *b3/2*d (µ=162) o3o3o3o5*a5/4*c *b3/2*d (µ=558) quasiregulars ```x3/2o3o3/2o5*a5*c *b3*d - (contains "2doe") o3/2x3o3/2o5*a5*c *b3*d - (contains "2tet") o3/2o3x3/2o5*a5*c *b3*d - (contains "2tet") ``` ```x3o3/2o3/2o5*a5*c *b3/2*d - (contains "2doe") o3x3/2o3/2o5*a5*c *b3/2*d - (contains "2tet") o3o3/2x3/2o5*a5*c *b3/2*d - (contains "2tet") ``` ```x3o3o3o5*a5/4*c *b3/2*d - (contains "2doe") o3x3o3o5*a5/4*c *b3/2*d - (contains "2tet") o3o3x3o5*a5/4*c *b3/2*d - (contains "2tet") o3o3o3x5*a5/4*c *b3/2*d - (contains "2tet") ``` otherWythoffians ```x3/2x3o3/2o5*a5*c *b3*d - [Grünbaumian] x3/2o3x3/2o5*a5*c *b3*d - o3/2x3x3/2o5*a5*c *b3*d - o3/2o3x3/2x5*a5*c *b3*d - [Grünbaumian] x3/2x3x3/2o5*a5*c *b3*d - [Grünbaumian] x3/2o3x3/2x5*a5*c *b3*d - [Grünbaumian] o3/2x3x3/2x5*a5*c *b3*d - [Grünbaumian] x3/2x3x3/2x5*a5*c *b3*d - [Grünbaumian] ``` ```x3x3/2o3/2o5*a5*c *b3/2*d - x3o3/2x3/2o5*a5*c *b3/2*d - o3x3/2x3/2o5*a5*c *b3/2*d - [Grünbaumian] o3o3/2x3/2x5*a5*c *b3/2*d - [Grünbaumian] x3x3/2x3/2o5*a5*c *b3/2*d - [Grünbaumian] x3o3/2x3/2x5*a5*c *b3/2*d - [Grünbaumian] o3x3/2x3/2x5*a5*c *b3/2*d - [Grünbaumian] x3x3/2x3/2x5*a5*c *b3/2*d - [Grünbaumian] ``` ```x3x3o3o5*a5/4*c *b3/2*d - x3o3x3o5*a5/4*c *b3/2*d - [Grünbaumian] x3o3o3x5*a5/4*c *b3/2*d - o3x3x3o5*a5/4*c *b3/2*d - o3x3o3x5*a5/4*c *b3/2*d - [Grünbaumian] o3o3x3x5*a5/4*c *b3/2*d - x3x3x3o5*a5/4*c *b3/2*d - [Grünbaumian] x3x3o3x5*a5/4*c *b3/2*d - [Grünbaumian] x3o3x3x5*a5/4*c *b3/2*d - [Grünbaumian] o3x3x3x5*a5/4*c *b3/2*d - [Grünbaumian] x3x3x3x5*a5/4*c *b3/2*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3/2o3/2o3o5*a5/4*c *b3*d (µ=642) o3o3o3/2o5/4*a5/4*c *b3*d (µ=1122) o3/2o3/2o3/2o5/4*a5/4*c *b3/2*d (µ=3438) quasiregulars ```x3/2o3/2o3o5*a5/4*c *b3*d - (contains "2doe") o3/2x3/2o3o5*a5/4*c *b3*d - (contains "2tet") o3/2o3/2x3o5*a5/4*c *b3*d - (contains "2tet") o3/2o3/2o3x5*a5/4*c *b3*d - (contains "2tet") ``` ```x3o3o3/2o5/4*a5/4*c *b3*d - (contains "2doe") o3x3o3/2o5/4*a5/4*c *b3*d - (contains "2tet") o3o3x3/2o5/4*a5/4*c *b3*d - (contains "2tet") ``` ```x3/2o3/2o3/2o5/4*a5/4*c *b3/2*d - (contains "2doe") o3/2x3/2o3/2o5/4*a5/4*c *b3/2*d - (contains "2tet") o3/2o3/2x3/2o5/4*a5/4*c *b3/2*d - (contains "2tet") ``` otherWythoffians ```x3/2x3/2o3o5*a5/4*c *b3*d - [Grünbaumian] x3/2o3/2x3o5*a5/4*c *b3*d - [Grünbaumian] x3/2o3/2o3x5*a5/4*c *b3*d - o3/2x3/2x3o5*a5/4*c *b3*d - [Grünbaumian] o3/2x3/2o3x5*a5/4*c *b3*d - o3/2o3/2x3x5*a5/4*c *b3*d - x3/2x3/2x3o5*a5/4*c *b3*d - [Grünbaumian] x3/2x3/2o3x5*a5/4*c *b3*d - [Grünbaumian] x3/2o3/2x3x5*a5/4*c *b3*d - [Grünbaumian] o3/2x3/2x3x5*a5/4*c *b3*d - [Grünbaumian] x3/2x3/2x3x5*a5/4*c *b3*d - [Grünbaumian] ``` ```x3x3o3/2o5/4*a5/4*c *b3*d - x3o3x3/2o5/4*a5/4*c *b3*d - [Grünbaumian] o3x3x3/2o5/4*a5/4*c *b3*d - o3o3x3/2x5/4*a5/4*c *b3*d - [Grünbaumian] x3x3x3/2o5/4*a5/4*c *b3*d - [Grünbaumian] x3o3x3/2x5/4*a5/4*c *b3*d - [Grünbaumian] x3x3x3/2x5/4*a5/4*c *b3*d - [Grünbaumian] ``` ```x3/2x3/2o3/2o5/4*a5/4*c *b3/2*d - [Grünbaumian] x3/2o3/2x3/2o5/4*a5/4*c *b3/2*d - [Grünbaumian] o3/2x3/2x3/2o5/4*a5/4*c *b3/2*d - [Grünbaumian] o3/2o3/2x3/2x5/4*a5/4*c *b3/2*d - [Grünbaumian] x3/2x3/2x3/2o5/4*a5/4*c *b3/2*d - [Grünbaumian] x3/2o3/2x3/2x5/4*a5/4*c *b3/2*d - [Grünbaumian] o3/2x3/2x3/2x5/4*a5/4*c *b3/2*d - [Grünbaumian] x3/2x3/2x3/2x5/4*a5/4*c *b3/2*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o3/2o5/2*a5/2*c *b3*d   (up)

 o3o3o3/2o5/2*a5/2*c *b3*d (µ=18) o3o3o3o5/3*a5/2*c *b3/2*d (µ=222) o3/2o3o3o5/2*a5/3*c *b3/2*d (µ=978) quasiregulars ```x3o3o3/2o5/2*a5/2*c *b3*d - (contains "2gissid") o3x3o3/2o5/2*a5/2*c *b3*d - (contains "2tet") o3o3x3/2o5/2*a5/2*c *b3*d - (contains "2tet") ``` ```x3o3o3o5/3*a5/2*c *b3/2*d - (contains "2gissid") o3x3o3o5/3*a5/2*c *b3/2*d - (contains "2tet") o3o3x3o5/3*a5/2*c *b3/2*d - (contains "2tet") o3o3o3x5/3*a5/2*c *b3/2*d - (contains "2tet") ``` ```x3/2o3o3o5/2*a5/3*c *b3/2*d - (contains "2gissid") o3/2x3o3o5/2*a5/3*c *b3/2*d - (contains "2tet") o3/2o3x3o5/2*a5/3*c *b3/2*d - (contains "2tet") o3/2o3o3x5/2*a5/3*c *b3/2*d - (contains "2tet") ``` otherWythoffians ```x3x3o3/2o5/2*a5/2*c *b3*d - x3o3x3/2o5/2*a5/2*c *b3*d - [Grünbaumian] o3x3x3/2o5/2*a5/2*c *b3*d - o3o3x3/2x5/2*a5/2*c *b3*d - [Grünbaumian] x3x3x3/2o5/2*a5/2*c *b3*d - [Grünbaumian] x3o3x3/2x5/2*a5/2*c *b3*d - [Grünbaumian] o3x3x3/2x5/2*a5/2*c *b3*d - [Grünbaumian] x3x3x3/2x5/2*a5/2*c *b3*d - [Grünbaumian] ``` ```x3x3o3o5/3*a5/2*c *b3/2*d - x3o3x3o5/3*a5/2*c *b3/2*d - [Grünbaumian] x3o3o3x5/3*a5/2*c *b3/2*d - o3x3x3o5/3*a5/2*c *b3/2*d - o3x3o3x5/3*a5/2*c *b3/2*d - [Grünbaumian] o3o3x3x5/3*a5/2*c *b3/2*d - x3x3x3o5/3*a5/2*c *b3/2*d - [Grünbaumian] x3x3o3x5/3*a5/2*c *b3/2*d - [Grünbaumian] x3o3x3x5/3*a5/2*c *b3/2*d - [Grünbaumian] o3x3x3x5/3*a5/2*c *b3/2*d - [Grünbaumian] x3x3x3x5/3*a5/2*c *b3/2*d - [Grünbaumian] ``` ```x3/2x3o3o5/2*a5/3*c *b3/2*d - [Grünbaumian] x3/2o3x3o5/2*a5/3*c *b3/2*d - x3/2o3o3x5/2*a5/3*c *b3/2*d - [Grünbaumian] o3/2x3x3o5/2*a5/3*c *b3/2*d - o3/2x3o3x5/2*a5/3*c *b3/2*d - [Grünbaumian] o3/2o3x3x5/2*a5/3*c *b3/2*d - x3/2x3x3o5/2*a5/3*c *b3/2*d - [Grünbaumian] x3/2x3o3x5/2*a5/3*c *b3/2*d - [Grünbaumian] x3/2o3x3x5/2*a5/3*c *b3/2*d - [Grünbaumian] o3/2x3x3x5/2*a5/3*c *b3/2*d - [Grünbaumian] x3/2x3x3x5/2*a5/3*c *b3/2*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3/2o3o3/2o5/3*a5/3*c *b3*d (µ=1182) o3/2o3/2o3/2o5/2*a5/2*c *b3/2*d (µ=1662) o3o3/2o3/2o5/3*a5/3*c *b3/2*d (µ=1938) quasiregulars ```x3/2o3o3/2o5/3*a5/3*c *b3*d - (contains "2gissid") o3/2x3o3/2o5/3*a5/3*c *b3*d - (contains "2tet") o3/2o3x3/2o5/3*a5/3*c *b3*d - (contains "2tet") ``` ```x3/2o3/2o3/2o5/2*a5/2*c *b3/2*d - (contains "2gissid") o3/2x3/2o3/2o5/2*a5/2*c *b3/2*d - (contains "2tet") o3/2o3/2x3/2o5/2*a5/2*c *b3/2*d - (contains "2tet") ``` ```x3o3/2o3/2o5/3*a5/3*c *b3/2*d - (contains "2gissid") o3x3/2o3/2o5/3*a5/3*c *b3/2*d - (contains "2tet") o3o3/2x3/2o5/3*a5/3*c *b3/2*d - (contains "2tet") ``` otherWythoffians ```x3/2x3o3/2o5/3*a5/3*c *b3*d - [Grünbaumian] x3/2o3x3/2o5/3*a5/3*c *b3*d - o3/2x3x3/2o5/3*a5/3*c *b3*d - o3/2o3x3/2x5/3*a5/3*c *b3*d - [Grünbaumian] x3/2x3x3/2o5/3*a5/3*c *b3*d - [Grünbaumian] x3/2o3x3/2x5/3*a5/3*c *b3*d - [Grünbaumian] o3/2x3x3/2x5/3*a5/3*c *b3*d - [Grünbaumian] x3/2x3x3/2x5/3*a5/3*c *b3*d - [Grünbaumian] ``` ```x3/2x3/2o3/2o5/2*a5/2*c *b3/2*d - [Grünbaumian] x3/2o3/2x3/2o5/2*a5/2*c *b3/2*d - [Grünbaumian] o3/2x3/2x3/2o5/2*a5/2*c *b3/2*d - [Grünbaumian] o3/2o3/2x3/2x5/2*a5/2*c *b3/2*d - [Grünbaumian] x3/2x3/2x3/2o5/2*a5/2*c *b3/2*d - [Grünbaumian] x3/2o3/2x3/2x5/2*a5/2*c *b3/2*d - [Grünbaumian] o3/2x3/2x3/2x5/2*a5/2*c *b3/2*d - [Grünbaumian] x3/2x3/2x3/2x5/2*a5/2*c *b3/2*d - [Grünbaumian] ``` ```x3x3/2o3/2o5/3*a5/3*c *b3/2*d - x3o3/2x3/2o5/3*a5/3*c *b3/2*d - o3x3/2x3/2o5/3*a5/3*c *b3/2*d - [Grünbaumian] o3o3/2x3/2x5/3*a5/3*c *b3/2*d - [Grünbaumian] x3x3/2x3/2o5/3*a5/3*c *b3/2*d - [Grünbaumian] x3o3/2x3/2x5/3*a5/3*c *b3/2*d - [Grünbaumian] o3x3/2x3/2x5/3*a5/3*c *b3/2*d - [Grünbaumian] x3x3/2x3/2x5/3*a5/3*c *b3/2*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o3o3*a5/2*c *b5/4*d   (up)

 o3o3o3o3*a5/2*c *b5/4*d (µ=80) o3o3o3/2o3/2*a5/2*c *b5*d (µ=160) o3o3/2o3o3/2*a5/3*c *b5*d (µ=560) quasiregulars ```x3o3o3o3*a5/2*c *b5/4*d - (contains "2gike") o3x3o3o3*a5/2*c *b5/4*d - (contains "2ike") ``` ```x3o3o3/2o3/2*a5/2*c *b5*d - (contains "2gike") o3x3o3/2o3/2*a5/2*c *b5*d - (contains "2ike") o3o3o3/2x3/2*a5/2*c *b5*d - (contains "2ike") ``` ```x3o3/2o3o3/2*a5/3*c *b5*d - (contains "2gike") o3x3/2o3o3/2*a5/3*c *b5*d - (contains "2ike") ``` otherWythoffians ```x3x3o3o3*a5/2*c *b5/4*d - x3o3x3o3*a5/2*c *b5/4*d - [Grünbaumian] o3x3o3x3*a5/2*c *b5/4*d - [Grünbaumian] x3x3x3o3*a5/2*c *b5/4*d - [Grünbaumian] x3x3o3x3*a5/2*c *b5/4*d - [Grünbaumian] x3x3x3x3*a5/2*c *b5/4*d - [Grünbaumian] ``` ```x3x3o3/2o3/2*a5/2*c *b5*d - x3o3x3/2o3/2*a5/2*c *b5*d - [Grünbaumian] x3o3o3/2x3/2*a5/2*c *b5*d - [Grünbaumian] o3x3o3/2x3/2*a5/2*c *b5*d - x3x3x3/2o3/2*a5/2*c *b5*d - [Grünbaumian] x3x3o3/2x3/2*a5/2*c *b5*d - [Grünbaumian] x3o3x3/2x3/2*a5/2*c *b5*d - [Grünbaumian] x3x3x3/2x3/2*a5/2*c *b5*d - [Grünbaumian] ``` ```x3x3/2o3o3/2*a5/3*c *b5*d - x3o3/2x3o3/2*a5/3*c *b5*d - x3o3/2o3x3/2*a5/3*c *b5*d - [Grünbaumian] o3x3/2o3x3/2*a5/3*c *b5*d - x3x3/2x3o3/2*a5/3*c *b5*d - [Grünbaumian] x3x3/2o3x3/2*a5/3*c *b5*d - [Grünbaumian] x3x3/2x3x3/2*a5/3*c *b5*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o3/2o3/2o3*a5/3*c *b5/4*d (µ=1600) o3/2o3/2o3/2o3/2*a5/2*c *b5/4*d (µ=2480) quasiregulars ```x3o3/2o3/2o3*a5/3*c *b5/4*d - (contains "2gike") o3x3/2o3/2o3*a5/3*c *b5/4*d - (contains "2ike") o3o3/2x3/2o3*a5/3*c *b5/4*d - (contains "2gike") ``` ```x3/2o3/2o3/2o3/2*a5/2*c *b5/4*d - (contains "2gike") o3/2x3/2o3/2o3/2*a5/2*c *b5/4*d - (contains "2ike") ``` otherWythoffians ```x3x3/2o3/2o3*a5/3*c *b5/4*d - x3o3/2x3/2o3*a5/3*c *b5/4*d - o3x3/2x3/2o3*a5/3*c *b5/4*d - [Grünbaumian] o3x3/2o3/2x3*a5/3*c *b5/4*d - [Grünbaumian] x3x3/2x3/2o3*a5/3*c *b5/4*d - [Grünbaumian] x3x3/2o3/2x3*a5/3*c *b5/4*d - [Grünbaumian] o3x3/2x3/2x3*a5/3*c *b5/4*d - [Grünbaumian] x3x3/2x3/2x3*a5/3*c *b5/4*d - [Grünbaumian] ``` ```x3/2x3/2o3/2o3/2*a5/2*c *b5/4*d - [Grünbaumian] x3/2o3/2x3/2o3/2*a5/2*c *b5/4*d - [Grünbaumian] o3/2x3/2o3/2x3/2*a5/2*c *b5/4*d - [Grünbaumian] x3/2x3/2x3/2o3/2*a5/2*c *b5/4*d - [Grünbaumian] x3/2x3/2o3/2x3/2*a5/2*c *b5/4*d - [Grünbaumian] x3/2x3/2x3/2x3/2*a5/2*c *b5/4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3/2o3/2o5o5*a3/2*c *b5*d   (up)

 o3/2o3/2o5o5*a3/2*c *b5*d (µ=6) o3o3o5o5*a3/2*c *b5/4*d (µ=234) quasiregulars ```x3/2o3/2o5o5*a3/2*c *b5*d - (contains "2tet") o3/2o3/2o5x5*a3/2*c *b5*d - (contains "2doe") ``` ```x3o3o5o5*a3/2*c *b5/4*d - (contains "2tet") o3x3o5o5*a3/2*c *b5/4*d - (contains "2tet") o3o3o5x5*a3/2*c *b5/4*d - (contains "2doe") ``` otherWythoffians ```x3/2x3/2o5o5*a3/2*c *b5*d - [Grünbaumian] x3/2o3/2o5x5*a3/2*c *b5*d - x3/2x3/2x5o5*a3/2*c *b5*d - [Grünbaumian] x3/2x3/2o5x5*a3/2*c *b5*d - [Grünbaumian] x3/2x3/2x5x5*a3/2*c *b5*d - [Grünbaumian] ``` ```x3x3o5o5*a3/2*c *b5/4*d - x3o3x5o5*a3/2*c *b5/4*d - [Grünbaumian] x3o3o5x5*a3/2*c *b5/4*d - o3x3o5x5*a3/2*c *b5/4*d - [Grünbaumian] x3x3x5o5*a3/2*c *b5/4*d - [Grünbaumian] x3x3o5x5*a3/2*c *b5/4*d - [Grünbaumian] x3o3x5x5*a3/2*c *b5/4*d - [Grünbaumian] x3x3x5x5*a3/2*c *b5/4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` o3o3o5/4o5/4*a3/2*c *b5*d (µ=966) o3/2o3/2o5/4o5/4*a3/2*c *b5/4*d (µ=3594) quasiregulars ```x3o3o5/4o5/4*a3/2*c *b5*d - (contains "2tet") o3x3o5/4o5/4*a3/2*c *b5*d - (contains "2tet") o3o3o5/4x5/4*a3/2*c *b5*d - (contains "2doe") ``` ```x3/2o3/2o5/4o5/4*a3/2*c *b5/4*d - (contains "2tet") o3/2o3/2o5/4x5/4*a3/2*c *b5/4*d - (contains "2doe") ``` otherWythoffians ```x3x3o5/4o5/4*a3/2*c *b5*d - x3o3x5/4o5/4*a3/2*c *b5*d - [Grünbaumian] x3o3o5/4x5/4*a3/2*c *b5*d - [Grünbaumian] o3x3o5/4x5/4*a3/2*c *b5*d - x3x3x5/4o5/4*a3/2*c *b5*d - [Grünbaumian] x3x3o5/4x5/4*a3/2*c *b5*d - [Grünbaumian] x3o3x5/4x5/4*a3/2*c *b5*d - [Grünbaumian] x3x3x5/4x5/4*a3/2*c *b5*d - [Grünbaumian] ``` ```x3/2x3/2o5/4o5/4*a3/2*c *b5/4*d - [Grünbaumian] x3/2o3/2o5/4x5/4*a3/2*c *b5/4*d - [Grünbaumian] x3/2x3/2x5/4o5/4*a3/2*c *b5/4*d - [Grünbaumian] x3/2x3/2o5/4x5/4*a3/2*c *b5/4*d - [Grünbaumian] x3/2x3/2x5/4x5/4*a3/2*c *b5/4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5/2o5/2*a3/2*c *b5/3*d   (up)

 o3o3o5/2o5/2*a3/2*c *b5/3*d (µ=534) o3o3/2o5/3o5/2*a3*c *b5/3*d (µ=666) quasiregulars ```x3o3o5/2o5/2*a3/2*c *b5/3*d - (contains "2tet") o3x3o5/2o5/2*a3/2*c *b5/3*d - (contains "2tet") o3o3o5/2x5/2*a3/2*c *b5/3*d - (contains "2gissid") ``` ```x3o3/2o5/3o5/2*a3*c *b5/3*d - (contains "2tet") o3x3/2o5/3o5/2*a3*c *b5/3*d - (contains "2tet") o3o3/2o5/3x5/2*a3*c *b5/3*d - (contains "2gissid") ``` otherWythoffians ```x3x3o5/2o5/2*a3/2*c *b5/3*d - x3o3x5/2o5/2*a3/2*c *b5/3*d - [Grünbaumian] x3o3o5/2x5/2*a3/2*c *b5/3*d - [Grünbaumian] o3x3o5/2x5/2*a3/2*c *b5/3*d - x3x3x5/2o5/2*a3/2*c *b5/3*d - [Grünbaumian] x3x3o5/2x5/2*a3/2*c *b5/3*d - [Grünbaumian] x3o3x5/2x5/2*a3/2*c *b5/3*d - [Grünbaumian] x3x3x5/2x5/2*a3/2*c *b5/3*d - [Grünbaumian] ``` ```x3x3/2o5/3o5/2*a3*c *b5/3*d - x3o3/2o5/3x5/2*a3*c *b5/3*d - [Grünbaumian] o3x3/2x5/3o5/2*a3*c *b5/3*d - [Grünbaumian] o3x3/2o5/3x5/2*a3*c *b5/3*d - x3x3/2x5/3o5/2*a3*c *b5/3*d - [Grünbaumian] x3x3/2o5/3x5/2*a3*c *b5/3*d - [Grünbaumian] o3x3/2x5/3x5/2*a3*c *b5/3*d - [Grünbaumian] x3x3/2x5/3x5/2*a3*c *b5/3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` o3/2o3/2o5/2o5/2*a3/2*c *b5/2*d (µ=1146) o3/2o3/2o5/3o5/3*a3/2*c *b5/3*d (µ=2454) quasiregulars ```x3/2o3/2o5/2o5/2*a3/2*c *b5/2*d - (contains "2tet") o3/2o3/2o5/2x5/2*a3/2*c *b5/2*d - (contains "2gissid") ``` ```x3/2o3/2o5/3o5/3*a3/2*c *b5/3*d - (contains "2tet") o3/2o3/2o5/3x5/3*a3/2*c *b5/3*d - (contains "2gissid") ``` otherWythoffians ```x3/2x3/2o5/2o5/2*a3/2*c *b5/2*d - [Grünbaumian] x3/2o3/2o5/2x5/2*a3/2*c *b5/2*d - [Grünbaumian] x3/2x3/2x5/2o5/2*a3/2*c *b5/2*d - [Grünbaumian] x3/2x3/2o5/2x5/2*a3/2*c *b5/2*d - [Grünbaumian] x3/2x3/2x5/2x5/2*a3/2*c *b5/2*d - [Grünbaumian] ``` ```x3/2x3/2o5/3o5/3*a3/2*c *b5/3*d - [Grünbaumian] x3/2o3/2o5/3x5/3*a3/2*c *b5/3*d - x3/2x3/2x5/3o5/3*a3/2*c *b5/3*d - [Grünbaumian] x3/2x3/2o5/3x5/3*a3/2*c *b5/3*d - [Grünbaumian] x3/2x3/2x5/3x5/3*a3/2*c *b5/3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5o5*a3/2*c *b5/3*d   (up)

 o3o3o5o5*a3/2*c *b5/3*d (µ=10) o3/2o3/2o5o5*a3/2*c *b5/2*d (µ=230) o3o3/2o5/4o5*a3*c *b5/3*d (µ=470) quasiregulars ```x3o3o5o5*a3/2*c *b5/3*d - (contains "2tet") o3x3o5o5*a3/2*c *b5/3*d - (contains "2tet") o3o3o5x5*a3/2*c *b5/3*d - (contains "2doe") ``` ```x3/2o3/2o5o5*a3/2*c *b5/2*d - (contains "2tet") o3/2x3/2o5o5*a3/2*c *b5/2*d - (contains "2tet") o3/2o3/2o5x5*a3/2*c *b5/2*d - (contains "2doe") ``` ```x3o3/2o5/4o5*a3*c *b5/3*d - (contains "2tet") o3x3/2o5/4o5*a3*c *b5/3*d - (contains "2tet") o3o3/2x5/4o5*a3*c *b5/3*d - (contains "2tet") o3o3/2o5/4x5*a3*c *b5/3*d - (contains "2doe") ``` otherWythoffians ```x3x3o5o5*a3/2*c *b5/3*d - x3o3x5o5*a3/2*c *b5/3*d - [Grünbaumian] x3o3o5x5*a3/2*c *b5/3*d - o3x3o5x5*a3/2*c *b5/3*d - x3x3x5o5*a3/2*c *b5/3*d - [Grünbaumian] x3x3o5x5*a3/2*c *b5/3*d - skiv datixathi x3o3x5x5*a3/2*c *b5/3*d - [Grünbaumian] x3x3x5x5*a3/2*c *b5/3*d - [Grünbaumian] ``` ```x3/2x3/2o5o5*a3/2*c *b5/2*d - [Grünbaumian] x3/2o3/2x5o5*a3/2*c *b5/2*d - [Grünbaumian] x3/2o3/2o5x5*a3/2*c *b5/2*d - o3/2x3/2o5x5*a3/2*c *b5/2*d - [Grünbaumian] x3/2x3/2x5o5*a3/2*c *b5/2*d - [Grünbaumian] x3/2x3/2o5x5*a3/2*c *b5/2*d - [Grünbaumian] x3/2o3/2x5x5*a3/2*c *b5/2*d - [Grünbaumian] x3/2x3/2x5x5*a3/2*c *b5/2*d - [Grünbaumian] ``` ```x3x3/2o5/4o5*a3*c *b5/3*d - x3o3/2x5/4o5*a3*c *b5/3*d - x3o3/2o5/4x5*a3*c *b5/3*d - o3x3/2x5/4o5*a3*c *b5/3*d - [Grünbaumian] o3x3/2o5/4x5*a3*c *b5/3*d - o3o3/2x5/4x5*a3*c *b5/3*d - [Grünbaumian] x3x3/2x5/4o5*a3*c *b5/3*d - [Grünbaumian] x3x3/2o5/4x5*a3*c *b5/3*d - x3o3/2x5/4x5*a3*c *b5/3*d - [Grünbaumian] o3x3/2x5/4x5*a3*c *b5/3*d - [Grünbaumian] x3x3/2x5/4x5*a3*c *b5/3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o3/2o5o5/4*a3*c *b5/2*d (µ=730) o3o3o5/4o5/4*a3/2*c *b5/2*d (µ=1190) o3/2o3/2o5/4o5/4*a3/2*c *b5/3*d (µ=3370) quasiregulars ```x3o3/2o5o5/4*a3*c *b5/2*d - (contains "2tet") o3x3/2o5o5/4*a3*c *b5/2*d - (contains "2tet") o3o3/2x5o5/4*a3*c *b5/2*d - (contains "2tet") o3o3/2o5x5/4*a3*c *b5/2*d - (contains "2doe") ``` ```x3o3o5/4o5/4*a3/2*c *b5/2*d - (contains "2tet") o3x3o5/4o5/4*a3/2*c *b5/2*d - (contains "2tet") o3o3o5/4x5/4*a3/2*c *b5/2*d - (contains "2doe") ``` ```x3/2o3/2o5/4o5/4*a3/2*c *b5/3*d - (contains "2tet") o3/2x3/2o5/4o5/4*a3/2*c *b5/3*d - (contains "2tet") o3/2o3/2o5/4x5/4*a3/2*c *b5/3*d - (contains "2doe") ``` otherWythoffians ```x3x3/2o5o5/4*a3*c *b5/2*d - x3o3/2x5o5/4*a3*c *b5/2*d - x3o3/2o5x5/4*a3*c *b5/2*d - [Grünbaumian] o3x3/2x5o5/4*a3*c *b5/2*d - [Grünbaumian] o3x3/2o5x5/4*a3*c *b5/2*d - [Grünbaumian] o3o3/2x5x5/4*a3*c *b5/2*d - x3x3/2x5o5/4*a3*c *b5/2*d - [Grünbaumian] x3x3/2o5x5/4*a3*c *b5/2*d - [Grünbaumian] x3o3/2x5x5/4*a3*c *b5/2*d - [Grünbaumian] o3x3/2x5x5/4*a3*c *b5/2*d - [Grünbaumian] x3x3/2x5x5/4*a3*c *b5/2*d - [Grünbaumian] ``` ```x3x3o5/4o5/4*a3/2*c *b5/2*d - x3o3x5/4o5/4*a3/2*c *b5/2*d - [Grünbaumian] x3o3o5/4x5/4*a3/2*c *b5/2*d - [Grünbaumian] o3x3o5/4x5/4*a3/2*c *b5/2*d - [Grünbaumian] x3x3x5/4o5/4*a3/2*c *b5/2*d - [Grünbaumian] x3x3o5/4x5/4*a3/2*c *b5/2*d - [Grünbaumian] x3o3x5/4x5/4*a3/2*c *b5/2*d - [Grünbaumian] x3x3x5/4x5/4*a3/2*c *b5/2*d - [Grünbaumian] ``` ```x3/2x3/2o5/4o5/4*a3/2*c *b5/3*d - [Grünbaumian] x3/2o3/2x5/4o5/4*a3/2*c *b5/3*d - [Grünbaumian] x3/2o3/2o5/4x5/4*a3/2*c *b5/3*d - [Grünbaumian] o3/2x3/2o5/4x5/4*a3/2*c *b5/3*d - [Grünbaumian] x3/2x3/2x5/4o5/4*a3/2*c *b5/3*d - [Grünbaumian] x3/2x3/2o5/4x5/4*a3/2*c *b5/3*d - [Grünbaumian] x3/2o3/2x5/4x5/4*a3/2*c *b5/3*d - [Grünbaumian] x3/2x3/2x5/4x5/4*a3/2*c *b5/3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5/3o5/3*a3/2*c *b5*d   (up)

 o3o3o5/3o5/3*a3/2*c *b5*d (µ=230) o3/2o3o5/3o5/2*a3*c *b5*d (µ=250) o3/2o3/2o5/2o5/2*a3/2*c *b5*d (µ=710) quasiregulars ```x3o3o5/3o5/3*a3/2*c *b5*d - (contains "2tet") o3x3o5/3o5/3*a3/2*c *b5*d - (contains "2tet") o3o3o5/3x5/3*a3/2*c *b5*d - (contains "2gissid") ``` ```x3/2o3o5/3o5/2*a3*c *b5*d - (contains "2tet") o3/2x3o5/3o5/2*a3*c *b5*d - (contains "2tet") o3/2o3x5/3o5/2*a3*c *b5*d - (contains "2tet") o3/2o3o5/3x5/2*a3*c *b5*d - (contains "2gissid") ``` ```x3/2o3/2o5/2o5/2*a3/2*c *b5*d - (contains "2tet") o3/2x3/2o5/2o5/2*a3/2*c *b5*d - (contains "2tet") o3/2o3/2o5/2x5/2*a3/2*c *b5*d - (contains "2gissid") ``` otherWythoffians ```x3x3o5/3o5/3*a3/2*c *b5*d - x3o3x5/3o5/3*a3/2*c *b5*d - [Grünbaumian] x3o3o5/3x5/3*a3/2*c *b5*d - o3x3o5/3x5/3*a3/2*c *b5*d - x3x3x5/3o5/3*a3/2*c *b5*d - [Grünbaumian] x3x3o5/3x5/3*a3/2*c *b5*d - gikkiv datixathi x3o3x5/3x5/3*a3/2*c *b5*d - [Grünbaumian] x3x3x5/3x5/3*a3/2*c *b5*d - [Grünbaumian] ``` ```x3/2x3o5/3o5/2*a3*c *b5*d - [Grünbaumian] x3/2o3x5/3o5/2*a3*c *b5*d - x3/2o3o5/3x5/2*a3*c *b5*d - [Grünbaumian] o3/2x3x5/3o5/2*a3*c *b5*d - o3/2x3o5/3x5/2*a3*c *b5*d - o3/2o3x5/3x5/2*a3*c *b5*d - x3/2x3x5/3o5/2*a3*c *b5*d - [Grünbaumian] x3/2x3o5/3x5/2*a3*c *b5*d - [Grünbaumian] x3/2o3x5/3x5/2*a3*c *b5*d - [Grünbaumian] o3/2x3x5/3x5/2*a3*c *b5*d - x3/2x3x5/3x5/2*a3*c *b5*d - [Grünbaumian] ``` ```x3/2x3/2o5/2o5/2*a3/2*c *b5*d - [Grünbaumian] x3/2o3/2x5/2o5/2*a3/2*c *b5*d - [Grünbaumian] x3/2o3/2o5/2x5/2*a3/2*c *b5*d - [Grünbaumian] o3/2x3/2o5/2x5/2*a3/2*c *b5*d - x3/2x3/2x5/2o5/2*a3/2*c *b5*d - [Grünbaumian] x3/2x3/2o5/2x5/2*a3/2*c *b5*d - [Grünbaumian] x3/2o3/2x5/2x5/2*a3/2*c *b5*d - [Grünbaumian] x3/2x3/2x5/2x5/2*a3/2*c *b5*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o3/2o5/3o5/2*a3*c *b5/4*d (µ=950) o3o3o5/2o5/2*a3/2*c *b5/4*d (µ=970) o3/2o3/2o5/3o5/3*a3/2*c *b5/4*d (µ=2890) quasiregulars ```x3o3/2o5/3o5/2*a3*c *b5/4*d - (contains "2tet") o3x3/2o5/3o5/2*a3*c *b5/4*d - (contains "2tet") o3o3/2x5/3o5/2*a3*c *b5/4*d - (contains "2tet") o3o3/2o5/3x5/2*a3*c *b5/4*d - (contains "2gissid") ``` ```x3o3o5/2o5/2*a3/2*c *b5/4*d - (contains "2tet") o3x3o5/2o5/2*a3/2*c *b5/4*d - (contains "2tet") o3o3o5/2x5/2*a3/2*c *b5/4*d - (contains "2gissid") ``` ```x3/2o3/2o5/3o5/3*a3/2*c *b5/4*d - (contains "2tet") o3/2x3/2o5/3o5/3*a3/2*c *b5/4*d - (contains "2tet") o3/2o3/2o5/3x5/3*a3/2*c *b5/4*d - (contains "2gissid") ``` otherWythoffians ```x3x3/2o5/3o5/2*a3*c *b5/4*d - x3o3/2x5/3o5/2*a3*c *b5/4*d - x3o3/2o5/3x5/2*a3*c *b5/4*d - [Grünbaumian] o3x3/2x5/3o5/2*a3*c *b5/4*d - [Grünbaumian] o3x3/2o5/3x5/2*a3*c *b5/4*d - [Grünbaumian] o3o3/2x5/3x5/2*a3*c *b5/4*d - x3x3/2x5/3o5/2*a3*c *b5/4*d - [Grünbaumian] x3x3/2o5/3x5/2*a3*c *b5/4*d - [Grünbaumian] x3o3/2x5/3x5/2*a3*c *b5/4*d - [Grünbaumian] o3x3/2x5/3x5/2*a3*c *b5/4*d - [Grünbaumian] x3x3/2x5/3x5/2*a3*c *b5/4*d - [Grünbaumian] ``` ```x3x3o5/2o5/2*a3/2*c *b5/4*d - x3o3x5/2o5/2*a3/2*c *b5/4*d - [Grünbaumian] x3o3o5/2x5/2*a3/2*c *b5/4*d - [Grünbaumian] o3x3o5/2x5/2*a3/2*c *b5/4*d - [Grünbaumian] x3x3x5/2o5/2*a3/2*c *b5/4*d - [Grünbaumian] x3x3o5/2x5/2*a3/2*c *b5/4*d - [Grünbaumian] x3o3x5/2x5/2*a3/2*c *b5/4*d - [Grünbaumian] x3x3x5/2x5/2*a3/2*c *b5/4*d - [Grünbaumian] ``` ```x3/2x3/2o5/3o5/3*a3/2*c *b5/4*d - [Grünbaumian] x3/2o3/2x5/3o5/3*a3/2*c *b5/4*d - [Grünbaumian] x3/2o3/2o5/3x5/3*a3/2*c *b5/4*d - o3/2x3/2o5/3x5/3*a3/2*c *b5/4*d - [Grünbaumian] x3/2x3/2x5/3o5/3*a3/2*c *b5/4*d - [Grünbaumian] x3/2x3/2o5/3x5/3*a3/2*c *b5/4*d - [Grünbaumian] x3/2o3/2x5/3x5/3*a3/2*c *b5/4*d - [Grünbaumian] x3/2x3/2x5/3x5/3*a3/2*c *b5/4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5o3o5*a3/2*c *b5/3*d   (up)

 o3o5o3o5*a3/2*c *b5/3*d (µ=56) o3/2o5o3/2o5*a3*c *b5/2*d (µ=296) o3/2o5o3o5/4*a3*c *b5/3*d (µ=424) quasiregulars ```x3o5o3o5*a3/2*c *b5/3*d - (contains "2gike") o3x5o3o5*a3/2*c *b5/3*d - (contains gacid) ``` ```x3/2o5o3/2o5*a3*c *b5/2*d - (contains "2gike") o3/2x5o3/2o5*a3*c *b5/2*d - (contains gacid) ``` ```x3/2o5o3o5/4*a3*c *b5/3*d - (contains "2gike") o3/2x5o3o5/4*a3*c *b5/3*d - (contains gacid) o3/2o5x3o5/4*a3*c *b5/3*d - (contains "2gike") o3/2o5o3x5/4*a3*c *b5/3*d - (contains gacid) ``` otherWythoffians ```x3x5o3o5*a3/2*c *b5/3*d - x3o5x3o5*a3/2*c *b5/3*d - [Grünbaumian] x3o5o3x5*a3/2*c *b5/3*d - o3x5o3x5*a3/2*c *b5/3*d - x3x5x3o5*a3/2*c *b5/3*d - [Grünbaumian] x3x5o3x5*a3/2*c *b5/3*d - x3x5x3x5*a3/2*c *b5/3*d - [Grünbaumian] ``` ```x3/2x5o3/2o5*a3*c *b5/2*d - [Grünbaumian] x3/2o5x3/2o5*a3*c *b5/2*d - x3/2o5o3/2x5*a3*c *b5/2*d - o3/2x5o3/2x5*a3*c *b5/2*d - [Grünbaumian] x3/2x5x3/2o5*a3*c *b5/2*d - [Grünbaumian] x3/2x5o3/2x5*a3*c *b5/2*d - [Grünbaumian] x3/2x5x3/2x5*a3*c *b5/2*d - [Grünbaumian] ``` ```x3/2x5o3o5/4*a3*c *b5/3*d - [Grünbaumian] x3/2o5x3o5/4*a3*c *b5/3*d - x3/2o5o3x5/4*a3*c *b5/3*d - [Grünbaumian] o3/2x5x3o5/4*a3*c *b5/3*d - o3/2x5o3x5/4*a3*c *b5/3*d - o3/2o5x3x5/4*a3*c *b5/3*d - x3/2x5x3o5/4*a3*c *b5/3*d - [Grünbaumian] x3/2x5o3x5/4*a3*c *b5/3*d - [Grünbaumian] x3/2o5x3x5/4*a3*c *b5/3*d - [Grünbaumian] o3/2x5x3x5/4*a3*c *b5/3*d - x3/2x5x3x5/4*a3*c *b5/3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o5o3/2o5/4*a3/2*c *b5/2*d (µ=664) o3o5/4o3o5/4*a3*c *b5/2*d (µ=1256) o3/2o5/4o3/2o5/4*a3/2*c *b5/3*d (µ=3416) quasiregulars ```x3o5o3/2o5/4*a3/2*c *b5/2*d - (contains "2gike") o3x5o3/2o5/4*a3/2*c *b5/2*d - (contains gacid) o3o5x3/2o5/4*a3/2*c *b5/2*d - (contains "2gike") o3o5o3/2x5/4*a3/2*c *b5/2*d - (contains gacid) ``` ```x3o5/4o3o5/4*a3*c *b5/2*d - (contains "2gike") o3x5/4o3o5/4*a3*c *b5/2*d - (contains gacid) ``` ```x3/2o5/4o3/2o5/4*a3/2*c *b5/3*d - (contains "2gike") o3/2x5/4o3/2o5/4*a3/2*c *b5/3*d - (contains gacid) ``` otherWythoffians ```x3x5o3/2o5/4*a3/2*c *b5/2*d - x3o5x3/2o5/4*a3/2*c *b5/2*d - [Grünbaumian] x3o5o3/2x5/4*a3/2*c *b5/2*d - [Grünbaumian] o3x5x3/2o5/4*a3/2*c *b5/2*d - o3x5o3/2x5/4*a3/2*c *b5/2*d - [Grünbaumian] o3o5x3/2x5/4*a3/2*c *b5/2*d - [Grünbaumian] x3x5x3/2o5/4*a3/2*c *b5/2*d - [Grünbaumian] x3x5o3/2x5/4*a3/2*c *b5/2*d - [Grünbaumian] x3o5x3/2x5/4*a3/2*c *b5/2*d - [Grünbaumian] o3x5x3/2x5/4*a3/2*c *b5/2*d - [Grünbaumian] x3x5x3/2x5/4*a3/2*c *b5/2*d - [Grünbaumian] ``` ```x3x5/4o3o5/4*a3*c *b5/2*d - x3o5/4x3o5/4*a3*c *b5/2*d - x3o5/4o3x5/4*a3*c *b5/2*d - [Grünbaumian] o3x5/4o3x5/4*a3*c *b5/2*d - [Grünbaumian] x3x5/4x3o5/4*a3*c *b5/2*d - [Grünbaumian] x3x5/4o3x5/4*a3*c *b5/2*d - [Grünbaumian] x3x5/4x3x5/4*a3*c *b5/2*d - [Grünbaumian] ``` ```x3/2x5/4o3/2o5/4*a3/2*c *b5/3*d - [Grünbaumian] x3/2o5/4x3/2o5/4*a3/2*c *b5/3*d - [Grünbaumian] x3/2o5/4o3/2x5/4*a3/2*c *b5/3*d - [Grünbaumian] o3/2x5/4o3/2x5/4*a3/2*c *b5/3*d - x3/2x5/4x3/2o5/4*a3/2*c *b5/3*d - [Grünbaumian] x3/2x5/4o3/2x5/4*a3/2*c *b5/3*d - [Grünbaumian] x3/2x5/4x3/2x5/4*a3/2*c *b5/3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5/2o3o5/2*a3*c *b5/4*d   (up)

 o3o5/2o3o5/2*a3*c *b5/4*d (µ=104) o3o5/2o3/2o5/3*a3*c *b5*d (µ=136) o3o5/3o3o5/3*a3/2*c *b5*d (µ=344) quasiregulars ```x3o5/2o3o5/2*a3*c *b5/4*d - (contains "2ike") o3x5/2o3o5/2*a3*c *b5/4*d - (contains cid) ``` ```x3o5/2o3/2o5/3*a3*c *b5*d - (contains "2ike") o3x5/2o3/2o5/3*a3*c *b5*d - (contains cid) o3o5/2x3/2o5/3*a3*c *b5*d - (contains "2ike") o3o5/2o3/2x5/3*a3*c *b5*d - (contains cid) ``` ```x3o5/3o3o5/3*a3/2*c *b5*d - (contains "2ike") o3x5/3o3o5/3*a3/2*c *b5*d - (contains cid) ``` otherWythoffians ```x3x5/2o3o5/2*a3*c *b5/4*d - x3o5/2x3o5/2*a3*c *b5/4*d - x3o5/2o3x5/2*a3*c *b5/4*d - [Grünbaumian] o3x5/2o3x5/2*a3*c *b5/4*d - [Grünbaumian] x3x5/2x3o5/2*a3*c *b5/4*d - [Grünbaumian] x3x5/2o3x5/2*a3*c *b5/4*d - [Grünbaumian] x3x5/2x3x5/2*a3*c *b5/4*d - [Grünbaumian] ``` ```x3x5/2o3/2o5/3*a3*c *b5*d - x3o5/2x3/2o5/3*a3*c *b5*d - x3o5/2o3/2x5/3*a3*c *b5*d - o3x5/2x3/2o5/3*a3*c *b5*d - [Grünbaumian] o3x5/2o3/2x5/3*a3*c *b5*d - o3o5/2x3/2x5/3*a3*c *b5*d - [Grünbaumian] x3x5/2x3/2o5/3*a3*c *b5*d - [Grünbaumian] x3x5/2o3/2x5/3*a3*c *b5*d - x3o5/2x3/2x5/3*a3*c *b5*d - [Grünbaumian] o3x5/2x3/2x5/3*a3*c *b5*d - [Grünbaumian] x3x5/2x3/2x5/3*a3*c *b5*d - [Grünbaumian] ``` ```x3x5/3o3o5/3*a3/2*c *b5*d - x3o5/3x3o5/3*a3/2*c *b5*d - [Grünbaumian] x3o5/3o3x5/3*a3/2*c *b5*d - o3x5/3o3x5/3*a3/2*c *b5*d - x3x5/3x3o5/3*a3/2*c *b5*d - [Grünbaumian] x3x5/3o3x5/3*a3/2*c *b5*d - x3x5/3x3x5/3*a3/2*c *b5*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3/2o5/2o3/2o5/2*a3/2*c *b5*d (µ=824) o3o5/3o3/2o5/2*a3/2*c *b5/4*d (µ=1816) o3/2o5/3o3/2o5/3*a3*c *b5/4*d (µ=2024) quasiregulars ```x3/2o5/2o3/2o5/2*a3/2*c *b5*d - (contains "2ike") o3/2x5/2o3/2o5/2*a3/2*c *b5*d - (contains cid) ``` ```x3o5/3o3/2o5/2*a3/2*c *b5/4*d - (contains "2ike") o3x5/3o3/2o5/2*a3/2*c *b5/4*d - (contains cid) o3o5/3x3/2o5/2*a3/2*c *b5/4*d - (contains "2ike") o3o5/3o3/2x5/2*a3/2*c *b5/4*d - (contains cid) ``` ```x3/2o5/3o3/2o5/3*a3*c *b5/4*d - (contains "2ike") o3/2x5/3o3/2o5/3*a3*c *b5/4*d - (contains cid) ``` otherWythoffians ```x3/2x5/2o3/2o5/2*a3/2*c *b5*d - [Grünbaumian] x3/2o5/2x3/2o5/2*a3/2*c *b5*d - [Grünbaumian] x3/2o5/2o3/2x5/2*a3/2*c *b5*d - [Grünbaumian] o3/2x5/2o3/2x5/2*a3/2*c *b5*d - x3/2x5/2x3/2o5/2*a3/2*c *b5*d - [Grünbaumian] x3/2x5/2o3/2x5/2*a3/2*c *b5*d - [Grünbaumian] x3/2x5/2x3/2x5/2*a3/2*c *b5*d - [Grünbaumian] ``` ```x3x5/3o3/2o5/2*a3/2*c *b5/4*d - x3o5/3x3/2o5/2*a3/2*c *b5/4*d - [Grünbaumian] x3o5/3o3/2x5/2*a3/2*c *b5/4*d - [Grünbaumian] o3x5/3x3/2o5/2*a3/2*c *b5/4*d - o3x5/3o3/2x5/2*a3/2*c *b5/4*d - [Grünbaumian] o3o5/3x3/2x5/2*a3/2*c *b5/4*d - [Grünbaumian] x3x5/3x3/2o5/2*a3/2*c *b5/4*d - [Grünbaumian] x3x5/3o3/2x5/2*a3/2*c *b5/4*d - [Grünbaumian] x3o5/3x3/2x5/2*a3/2*c *b5/4*d - [Grünbaumian] o3x5/3x3/2x5/2*a3/2*c *b5/4*d - [Grünbaumian] x3x5/3x3/2x5/2*a3/2*c *b5/4*d - [Grünbaumian] ``` ```x3/2x5/3o3/2o5/3*a3*c *b5/4*d - [Grünbaumian] x3/2o5/3x3/2o5/3*a3*c *b5/4*d - x3/2o5/3o3/2x5/3*a3*c *b5/4*d - o3/2x5/3o3/2x5/3*a3*c *b5/4*d - [Grünbaumian] x3/2x5/3x3/2o5/3*a3*c *b5/4*d - [Grünbaumian] x3/2x5/3o3/2x5/3*a3*c *b5/4*d - [Grünbaumian] x3/2x5/3x3/2x5/3*a3*c *b5/4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3/2o3/2o5o5*a5/4*c *b5*d   (up)

 o3/2o3/2o5o5*a5/4*c *b5*d (µ=92) o3o3/2o5o5/4*a5*c *b5*d (µ=148) o3o3/2o5/4o5*a5*c *b5/4*d (µ=572) quasiregulars ```x3/2o3/2o5o5*a5/4*c *b5*d - (contains "2gad") o3/2x3/2o5o5*a5/4*c *b5*d - (contains "2gike") o3/2o3/2o5x5*a5/4*c *b5*d - (contains "2doe") ``` ```x3o3/2o5o5/4*a5*c *b5*d - (contains "2gad") o3x3/2o5o5/4*a5*c *b5*d - (contains "2gike") o3o3/2x5o5/4*a5*c *b5*d - (contains "2gad") o3o3/2o5x5/4*a5*c *b5*d - (contains "2doe") ``` ```x3o3/2o5/4o5*a5*c *b5/4*d - (contains "2gad") o3x3/2o5/4o5*a5*c *b5/4*d - (contains "2gike") o3o3/2x5/4o5*a5*c *b5/4*d - (contains "2gad") o3o3/2o5/4x5*a5*c *b5/4*d - (contains "2doe") ``` otherWythoffians ```x3/2x3/2o5o5*a5/4*c *b5*d - [Grünbaumian] x3/2o3/2x5o5*a5/4*c *b5*d - [Grünbaumian] x3/2o3/2o5x5*a5/4*c *b5*d - o3/2x3/2o5x5*a5/4*c *b5*d - x3/2x3/2x5o5*a5/4*c *b5*d - [Grünbaumian] x3/2x3/2o5x5*a5/4*c *b5*d - [Grünbaumian] x3/2o3/2x5x5*a5/4*c *b5*d - [Grünbaumian] x3/2x3/2x5x5*a5/4*c *b5*d - [Grünbaumian] ``` ```x3x3/2o5o5/4*a5*c *b5*d - x3o3/2x5o5/4*a5*c *b5*d - x3o3/2o5x5/4*a5*c *b5*d - [Grünbaumian] o3x3/2x5o5/4*a5*c *b5*d - [Grünbaumian] o3x3/2o5x5/4*a5*c *b5*d - o3o3/2x5x5/4*a5*c *b5*d - x3x3/2x5o5/4*a5*c *b5*d - [Grünbaumian] x3x3/2o5x5/4*a5*c *b5*d - [Grünbaumian] x3o3/2x5x5/4*a5*c *b5*d - [Grünbaumian] o3x3/2x5x5/4*a5*c *b5*d - [Grünbaumian] x3x3/2x5x5/4*a5*c *b5*d - [Grünbaumian] ``` ```x3x3/2o5/4o5*a5*c *b5/4*d - x3o3/2x5/4o5*a5*c *b5/4*d - x3o3/2o5/4x5*a5*c *b5/4*d - o3x3/2x5/4o5*a5*c *b5/4*d - [Grünbaumian] o3x3/2o5/4x5*a5*c *b5/4*d - [Grünbaumian] o3o3/2x5/4x5*a5*c *b5/4*d - [Grünbaumian] x3x3/2x5/4o5*a5*c *b5/4*d - [Grünbaumian] x3x3/2o5/4x5*a5*c *b5/4*d - [Grünbaumian] x3o3/2x5/4x5*a5*c *b5/4*d - [Grünbaumian] o3x3/2x5/4x5*a5*c *b5/4*d - [Grünbaumian] x3x3/2x5/4x5*a5*c *b5/4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o3o5o5*a5/4*c *b5/4*d (µ=628) o3o3o5/4o5/4*a5/4*c *b5*d (µ=1052) o3/2o3/2o5/4o5/4*a5/4*c *b5/4*d (µ=3988) quasiregulars ```x3o3o5o5*a5/4*c *b5/4*d - (contains "2gad") o3x3o5o5*a5/4*c *b5/4*d - (contains "2gike") o3o3o5x5*a5/4*c *b5/4*d - (contains "2doe") ``` ```x3o3o5/4o5/4*a5/4*c *b5*d - (contains "2gad") o3x3o5/4o5/4*a5/4*c *b5*d - (contains "2gike") o3o3o5/4x5/4*a5/4*c *b5*d - (contains "2doe") ``` ```x3/2o3/2o5/4o5/4*a5/4*c *b5/4*d - (contains "2gad") o3/2x3/2o5/4o5/4*a5/4*c *b5/4*d - (contains "2gike") o3/2o3/2o5/4x5/4*a5/4*c *b5/4*d - (contains "2doe") ``` otherWythoffians ```x3x3o5o5*a5/4*c *b5/4*d - x3o3x5o5*a5/4*c *b5/4*d - [Grünbaumian] x3o3o5x5*a5/4*c *b5/4*d - o3x3o5x5*a5/4*c *b5/4*d - [Grünbaumian] x3x3x5o5*a5/4*c *b5/4*d - [Grünbaumian] x3x3o5x5*a5/4*c *b5/4*d - [Grünbaumian] x3o3x5x5*a5/4*c *b5/4*d - [Grünbaumian] x3x3x5x5*a5/4*c *b5/4*d - [Grünbaumian] ``` ```x3x3o5/4o5/4*a5/4*c *b5*d - x3o3x5/4o5/4*a5/4*c *b5*d - [Grünbaumian] x3o3o5/4x5/4*a5/4*c *b5*d - [Grünbaumian] o3x3o5/4x5/4*a5/4*c *b5*d - x3x3x5/4o5/4*a5/4*c *b5*d - [Grünbaumian] x3x3o5/4x5/4*a5/4*c *b5*d - [Grünbaumian] x3o3x5/4x5/4*a5/4*c *b5*d - [Grünbaumian] x3x3x5/4x5/4*a5/4*c *b5*d - [Grünbaumian] ``` ```x3/2x3/2o5/4o5/4*a5/4*c *b5/4*d - [Grünbaumian] x3/2o3/2x5/4o5/4*a5/4*c *b5/4*d - [Grünbaumian] x3/2o3/2o5/4x5/4*a5/4*c *b5/4*d - [Grünbaumian] o3/2x3/2o5/4x5/4*a5/4*c *b5/4*d - [Grünbaumian] x3/2x3/2x5/4o5/4*a5/4*c *b5/4*d - [Grünbaumian] x3/2x3/2o5/4x5/4*a5/4*c *b5/4*d - [Grünbaumian] x3/2o3/2x5/4x5/4*a5/4*c *b5/4*d - [Grünbaumian] x3/2x3/2x5/4x5/4*a5/4*c *b5/4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5/2o5/2*a5/2*c *b5/3*d   (up)

 o3o3o5/2o5/2*a5/2*c *b5/3*d (µ=52) o3o3o5/3o5/3*a5/2*c *b5/2*d (µ=188) o3/2o3/2o5/2o5/2*a5/2*c *b5/2*d (µ=668) quasiregulars ```x3o3o5/2o5/2*a5/2*c *b5/3*d - (contains "2sissid") o3x3o5/2o5/2*a5/2*c *b5/3*d - (contains "2ike") o3o3o5/2x5/2*a5/2*c *b5/3*d - (contains "2sissid") ``` ```x3o3o5/3o5/3*a5/2*c *b5/2*d - (contains "2sissid") o3x3o5/3o5/3*a5/2*c *b5/2*d - (contains "2ike") o3o3o5/3x5/3*a5/2*c *b5/2*d - (contains "2sissid") ``` ```x3/2o3/2o5/2o5/2*a5/2*c *b5/2*d - (contains "2sissid") o3/2x3/2o5/2o5/2*a5/2*c *b5/2*d - (contains "2ike") o3/2o3/2o5/2x5/2*a5/2*c *b5/2*d - (contains "2sissid") ``` otherWythoffians ```x3x3o5/2o5/2*a5/2*c *b5/3*d - x3o3x5/2o5/2*a5/2*c *b5/3*d - [Grünbaumian] x3o3o5/2x5/2*a5/2*c *b5/3*d - [Grünbaumian] o3x3o5/2x5/2*a5/2*c *b5/3*d - x3x3x5/2o5/2*a5/2*c *b5/3*d - [Grünbaumian] x3x3o5/2x5/2*a5/2*c *b5/3*d - [Grünbaumian] x3o3x5/2x5/2*a5/2*c *b5/3*d - [Grünbaumian] x3x3x5/2x5/2*a5/2*c *b5/3*d - [Grünbaumian] ``` ```x3x3o5/3o5/3*a5/2*c *b5/2*d - x3o3x5/3o5/3*a5/2*c *b5/2*d - [Grünbaumian] x3o3o5/3x5/3*a5/2*c *b5/2*d - o3x3o5/3x5/3*a5/2*c *b5/2*d - [Grünbaumian] x3x3x5/3o5/3*a5/2*c *b5/2*d - [Grünbaumian] x3x3o5/3x5/3*a5/2*c *b5/2*d - [Grünbaumian] x3o3x5/3x5/3*a5/2*c *b5/2*d - [Grünbaumian] x3x3x5/3x5/3*a5/2*c *b5/2*d - [Grünbaumian] ``` ```x3/2x3/2o5/2o5/2*a5/2*c *b5/2*d - [Grünbaumian] x3/2o3/2x5/2o5/2*a5/2*c *b5/2*d - [Grünbaumian] x3/2o3/2o5/2x5/2*a5/2*c *b5/2*d - [Grünbaumian] o3/2x3/2o5/2x5/2*a5/2*c *b5/2*d - [Grünbaumian] x3/2x3/2x5/2o5/2*a5/2*c *b5/2*d - [Grünbaumian] x3/2x3/2o5/2x5/2*a5/2*c *b5/2*d - [Grünbaumian] x3/2o3/2x5/2x5/2*a5/2*c *b5/2*d - [Grünbaumian] x3/2x3/2x5/2x5/2*a5/2*c *b5/2*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o3/2o5/2o5/3*a5/3*c *b5/2*d (µ=1012) o3o3/2o5/3o5/2*a5/3*c *b5/3*d (µ=1148) o3/2o3/2o5/3o5/3*a5/2*c *b5/3*d (µ=1972) quasiregulars ```x3o3/2o5/2o5/3*a5/3*c *b5/2*d - (contains "2sissid") o3x3/2o5/2o5/3*a5/3*c *b5/2*d - (contains "2ike") o3o3/2x5/2o5/3*a5/3*c *b5/2*d - (contains "2sissid") o3o3/2o5/2x5/3*a5/3*c *b5/2*d - (contains "2sissid") ``` ```x3o3/2o5/3o5/2*a5/3*c *b5/3*d - (contains "2sissid") o3x3/2o5/3o5/2*a5/3*c *b5/3*d - (contains "2ike") o3o3/2x5/3o5/2*a5/3*c *b5/3*d - (contains "2sissid") o3o3/2o5/3x5/2*a5/3*c *b5/3*d - (contains "2sissid") ``` ```x3/2o3/2o5/3o5/3*a5/2*c *b5/3*d - (contains "2sissid") o3/2x3/2o5/3o5/3*a5/2*c *b5/3*d - (contains "2ike") o3/2o3/2o5/3x5/3*a5/2*c *b5/3*d - (contains "2sissid") ``` otherWythoffians ```x3x3/2o5/2o5/3*a5/3*c *b5/2*d - x3o3/2x5/2o5/3*a5/3*c *b5/2*d - x3o3/2o5/2x5/3*a5/3*c *b5/2*d - o3x3/2x5/2o5/3*a5/3*c *b5/2*d - [Grünbaumian] o3x3/2o5/2x5/3*a5/3*c *b5/2*d - [Grünbaumian] o3o3/2x5/2x5/3*a5/3*c *b5/2*d - [Grünbaumian] x3x3/2x5/2o5/3*a5/3*c *b5/2*d - [Grünbaumian] x3x3/2o5/2x5/3*a5/3*c *b5/2*d - [Grünbaumian] x3o3/2x5/2x5/3*a5/3*c *b5/2*d - [Grünbaumian] o3x3/2x5/2x5/3*a5/3*c *b5/2*d - [Grünbaumian] x3x3/2x5/2x5/3*a5/3*c *b5/2*d - [Grünbaumian] ``` ```x3x3/2o5/3o5/2*a5/3*c *b5/3*d - x3o3/2x5/3o5/2*a5/3*c *b5/3*d - x3o3/2o5/3x5/2*a5/3*c *b5/3*d - [Grünbaumian] o3x3/2x5/3o5/2*a5/3*c *b5/3*d - [Grünbaumian] o3x3/2o5/3x5/2*a5/3*c *b5/3*d - o3o3/2x5/3x5/2*a5/3*c *b5/3*d - x3x3/2x5/3o5/2*a5/3*c *b5/3*d - [Grünbaumian] x3x3/2o5/3x5/2*a5/3*c *b5/3*d - [Grünbaumian] x3o3/2x5/3x5/2*a5/3*c *b5/3*d - [Grünbaumian] o3x3/2x5/3x5/2*a5/3*c *b5/3*d - [Grünbaumian] x3x3/2x5/3x5/2*a5/3*c *b5/3*d - [Grünbaumian] ``` ```x3/2x3/2o5/3o5/3*a5/2*c *b5/3*d - [Grünbaumian] x3/2o3/2x5/3o5/3*a5/2*c *b5/3*d - [Grünbaumian] x3/2o3/2o5/3x5/3*a5/2*c *b5/3*d - o3/2x3/2o5/3x5/3*a5/2*c *b5/3*d - x3/2x3/2x5/3o5/3*a5/2*c *b5/3*d - [Grünbaumian] x3/2x3/2o5/3x5/3*a5/2*c *b5/3*d - [Grünbaumian] x3/2o3/2x5/3x5/3*a5/2*c *b5/3*d - [Grünbaumian] x3/2x3/2x5/3x5/3*a5/2*c *b5/3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5o5*a5/4*c *b5/3*d   (up)

 o3o3o5o5*a5/4*c *b5/3*d (µ=172) o3o3/2o5/4o5*a5*c *b5/3*d (µ=308) o3o3/2o5o5/4*a5*c *b5/2*d (µ=412) quasiregulars ```x3o3o5o5*a5/4*c *b5/3*d - (contains "2gad") o3x3o5o5*a5/4*c *b5/3*d - (contains "2gike") o3o3o5x5*a5/4*c *b5/3*d - (contains "2gad") ``` ```x3o3/2o5/4o5*a5*c *b5/3*d - (contains "2gad") o3x3/2o5/4o5*a5*c *b5/3*d - (contains "2gike") o3o3/2x5/4o5*a5*c *b5/3*d - (contains "2gad") o3o3/2o5/4x5*a5*c *b5/3*d - (contains "2gad") ``` ```x3o3/2o5o5/4*a5*c *b5/2*d - (contains "2gad") o3x3/2o5o5/4*a5*c *b5/2*d - (contains "2gike") o3o3/2x5o5/4*a5*c *b5/2*d - (contains "2gad") o3o3/2o5x5/4*a5*c *b5/2*d - (contains "2gad") ``` otherWythoffians ```x3x3o5o5*a5/4*c *b5/3*d - x3o3x5o5*a5/4*c *b5/3*d - [Grünbaumian] x3o3o5x5*a5/4*c *b5/3*d - o3x3o5x5*a5/4*c *b5/3*d - x3x3x5o5*a5/4*c *b5/3*d - [Grünbaumian] x3x3o5x5*a5/4*c *b5/3*d - x3o3x5x5*a5/4*c *b5/3*d - [Grünbaumian] x3x3x5x5*a5/4*c *b5/3*d - [Grünbaumian] ``` ```x3x3/2o5/4o5*a5*c *b5/3*d - x3o3/2x5/4o5*a5*c *b5/3*d - x3o3/2o5/4x5*a5*c *b5/3*d - o3x3/2x5/4o5*a5*c *b5/3*d - [Grünbaumian] o3x3/2o5/4x5*a5*c *b5/3*d - o3o3/2x5/4x5*a5*c *b5/3*d - [Grünbaumian] x3x3/2x5/4o5*a5*c *b5/3*d - [Grünbaumian] x3x3/2o5/4x5*a5*c *b5/3*d - x3o3/2x5/4x5*a5*c *b5/3*d - [Grünbaumian] o3x3/2x5/4x5*a5*c *b5/3*d - [Grünbaumian] x3x3/2x5/4x5*a5*c *b5/3*d - [Grünbaumian] ``` ```x3x3/2o5o5/4*a5*c *b5/2*d - x3o3/2x5o5/4*a5*c *b5/2*d - x3o3/2o5x5/4*a5*c *b5/2*d - [Grünbaumian] o3x3/2x5o5/4*a5*c *b5/2*d - [Grünbaumian] o3x3/2o5x5/4*a5*c *b5/2*d - [Grünbaumian] o3o3/2x5x5/4*a5*c *b5/2*d - x3x3/2x5o5/4*a5*c *b5/2*d - [Grünbaumian] x3x3/2o5x5/4*a5*c *b5/2*d - [Grünbaumian] x3o3/2x5x5/4*a5*c *b5/2*d - [Grünbaumian] o3x3/2x5x5/4*a5*c *b5/2*d - [Grünbaumian] x3x3/2x5x5/4*a5*c *b5/2*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3/2o3/2o5o5*a5/4*c *b5/2*d (µ=548) o3o3o5/4o5/4*a5/4*c *b5/2*d (µ=1508) o3/2o3/2o5/4o5/4*a5/4*c *b5/3*d (µ=3532) quasiregulars ```x3/2o3/2o5o5*a5/4*c *b5/2*d - (contains "2gad") o3/2x3/2o5o5*a5/4*c *b5/2*d - (contains "2gike") o3/2o3/2o5x5*a5/4*c *b5/2*d - (contains "2gad") ``` ```x3o3o5/4o5/4*a5/4*c *b5/2*d - (contains "2gad") o3x3o5/4o5/4*a5/4*c *b5/2*d - (contains "2gike") o3o3o5/4x5/4*a5/4*c *b5/2*d - (contains "2gad") ``` ```x3/2o3/2o5/4o5/4*a5/4*c *b5/3*d - (contains "2gad") o3/2x3/2o5/4o5/4*a5/4*c *b5/3*d - (contains "2gike") o3/2o3/2o5/4x5/4*a5/4*c *b5/3*d - (contains "2gad") ``` otherWythoffians ```x3/2x3/2o5o5*a5/4*c *b5/2*d - [Grünbaumian] x3/2o3/2x5o5*a5/4*c *b5/2*d - [Grünbaumian] x3/2o3/2o5x5*a5/4*c *b5/2*d - o3/2x3/2o5x5*a5/4*c *b5/2*d - [Grünbaumian] x3/2x3/2x5o5*a5/4*c *b5/2*d - [Grünbaumian] x3/2x3/2o5x5*a5/4*c *b5/2*d - [Grünbaumian] x3/2o3/2x5x5*a5/4*c *b5/2*d - [Grünbaumian] x3/2x3/2x5x5*a5/4*c *b5/2*d - [Grünbaumian] ``` ```x3x3o5/4o5/4*a5/4*c *b5/2*d - x3o3x5/4o5/4*a5/4*c *b5/2*d - [Grünbaumian] x3o3o5/4x5/4*a5/4*c *b5/2*d - [Grünbaumian] o3x3o5/4x5/4*a5/4*c *b5/2*d - [Grünbaumian] x3x3x5/4o5/4*a5/4*c *b5/2*d - [Grünbaumian] x3x3o5/4x5/4*a5/4*c *b5/2*d - [Grünbaumian] x3o3x5/4x5/4*a5/4*c *b5/2*d - [Grünbaumian] x3x3x5/4x5/4*a5/4*c *b5/2*d - [Grünbaumian] ``` ```x3/2x3/2o5/4o5/4*a5/4*c *b5/3*d - [Grünbaumian] x3/2o3/2x5/4o5/4*a5/4*c *b5/3*d - [Grünbaumian] x3/2o3/2o5/4x5/4*a5/4*c *b5/3*d - [Grünbaumian] o3/2x3/2o5/4x5/4*a5/4*c *b5/3*d - x3/2x3/2x5/4o5/4*a5/4*c *b5/3*d - [Grünbaumian] x3/2x3/2o5/4x5/4*a5/4*c *b5/3*d - [Grünbaumian] x3/2o3/2x5/4x5/4*a5/4*c *b5/3*d - [Grünbaumian] x3/2x3/2x5/4x5/4*a5/4*c *b5/3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5/3o5/3*a5/2*c *b5*d   (up)

 o3o3o5/3o5/3*a5/2*c *b5*d (µ=28) o3o3o5/2o5/2*a5/2*c *b5/4*d (µ=212) o3o3/2o5/2o5/3*a5/3*c *b5*d (µ=452) quasiregulars ```x3o3o5/3o5/3*a5/2*c *b5*d - (contains "2sissid") o3x3o5/3o5/3*a5/2*c *b5*d - (contains "2ike") o3o3o5/3x5/3*a5/2*c *b5*d - (contains "2sissid") ``` ```x3o3o5/2o5/2*a5/2*c *b5/4*d - (contains "2sissid") o3x3o5/2o5/2*a5/2*c *b5/4*d - (contains "2ike") o3o3o5/2x5/2*a5/2*c *b5/4*d - (contains "2sissid") ``` ```x3o3/2o5/2o5/3*a5/3*c *b5*d - (contains "2sissid") o3x3/2o5/2o5/3*a5/3*c *b5*d - (contains "2ike") o3o3/2x5/2o5/3*a5/3*c *b5*d - (contains "2sissid") o3o3/2o5/2x5/3*a5/3*c *b5*d - (contains "2sissid") ``` otherWythoffians ```x3x3o5/3o5/3*a5/2*c *b5*d - x3o3x5/3o5/3*a5/2*c *b5*d - [Grünbaumian] x3o3o5/3x5/3*a5/2*c *b5*d - o3x3o5/3x5/3*a5/2*c *b5*d - x3x3x5/3o5/3*a5/2*c *b5*d - [Grünbaumian] x3x3o5/3x5/3*a5/2*c *b5*d - x3o3x5/3x5/3*a5/2*c *b5*d - [Grünbaumian] x3x3x5/3x5/3*a5/2*c *b5*d - [Grünbaumian] ``` ```x3x3o5/2o5/2*a5/2*c *b5/4*d - x3o3x5/2o5/2*a5/2*c *b5/4*d - [Grünbaumian] x3o3o5/2x5/2*a5/2*c *b5/4*d - [Grünbaumian] o3x3o5/2x5/2*a5/2*c *b5/4*d - [Grünbaumian] x3x3x5/2o5/2*a5/2*c *b5/4*d - [Grünbaumian] x3x3o5/2x5/2*a5/2*c *b5/4*d - [Grünbaumian] x3o3x5/2x5/2*a5/2*c *b5/4*d - [Grünbaumian] x3x3x5/2x5/2*a5/2*c *b5/4*d - [Grünbaumian] ``` ```x3x3/2o5/2o5/3*a5/3*c *b5*d - x3o3/2x5/2o5/3*a5/3*c *b5*d - x3o3/2o5/2x5/3*a5/3*c *b5*d - o3x3/2x5/2o5/3*a5/3*c *b5*d - [Grünbaumian] o3x3/2o5/2x5/3*a5/3*c *b5*d - o3o3/2x5/2x5/3*a5/3*c *b5*d - [Grünbaumian] x3x3/2x5/2o5/3*a5/3*c *b5*d - [Grünbaumian] x3x3/2o5/2x5/3*a5/3*c *b5*d - x3o3/2x5/2x5/3*a5/3*c *b5*d - [Grünbaumian] o3x3/2x5/2x5/3*a5/3*c *b5*d - [Grünbaumian] x3x3/2x5/2x5/3*a5/3*c *b5*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3/2o3/2o5/2o5/2*a5/2*c *b5*d (µ=508) o3o3/2o5/3o5/2*a5/3*c *b5/4*d (µ=1708) o3/2o3/2o5/3o5/3*a5/2*c *b5/4*d (µ=2132) quasiregulars ```x3/2o3/2o5/2o5/2*a5/2*c *b5*d - (contains "2sissid") o3/2x3/2o5/2o5/2*a5/2*c *b5*d - (contains "2ike") o3/2o3/2o5/2x5/2*a5/2*c *b5*d - (contains "2sissid") ``` ```x3o3/2o5/3o5/2*a5/3*c *b5/4*d - (contains "2sissid") o3x3/2o5/3o5/2*a5/3*c *b5/4*d - (contains "2ike") o3o3/2x5/3o5/2*a5/3*c *b5/4*d - (contains "2sissid") o3o3/2o5/3x5/2*a5/3*c *b5/4*d - (contains "2sissid") ``` ```x3/2o3/2o5/3o5/3*a5/2*c *b5/4*d - (contains "2sissid") o3/2x3/2o5/3o5/3*a5/2*c *b5/4*d - (contains "2ike") o3/2o3/2o5/3x5/3*a5/2*c *b5/4*d - (contains "2sissid") ``` otherWythoffians ```x3/2x3/2o5/2o5/2*a5/2*c *b5*d - [Grünbaumian] x3/2o3/2x5/2o5/2*a5/2*c *b5*d - [Grünbaumian] x3/2o3/2o5/2x5/2*a5/2*c *b5*d - [Grünbaumian] o3/2x3/2o5/2x5/2*a5/2*c *b5*d - x3/2x3/2x5/2o5/2*a5/2*c *b5*d - [Grünbaumian] x3/2x3/2o5/2x5/2*a5/2*c *b5*d - [Grünbaumian] x3/2o3/2x5/2x5/2*a5/2*c *b5*d - [Grünbaumian] x3/2x3/2x5/2x5/2*a5/2*c *b5*d - [Grünbaumian] ``` ```x3x3/2o5/3o5/2*a5/3*c *b5/4*d - x3o3/2x5/3o5/2*a5/3*c *b5/4*d - x3o3/2o5/3x5/2*a5/3*c *b5/4*d - [Grünbaumian] o3x3/2x5/3o5/2*a5/3*c *b5/4*d - [Grünbaumian] o3x3/2o5/3x5/2*a5/3*c *b5/4*d - [Grünbaumian] o3o3/2x5/3x5/2*a5/3*c *b5/4*d - x3x3/2x5/3o5/2*a5/3*c *b5/4*d - [Grünbaumian] x3x3/2o5/3x5/2*a5/3*c *b5/4*d - [Grünbaumian] x3o3/2x5/3x5/2*a5/3*c *b5/4*d - [Grünbaumian] o3x3/2x5/3x5/2*a5/3*c *b5/4*d - [Grünbaumian] x3x3/2x5/3x5/2*a5/3*c *b5/4*d - [Grünbaumian] ``` ```x3/2x3/2o5/3o5/3*a5/2*c *b5/4*d - [Grünbaumian] x3/2o3/2x5/3o5/3*a5/2*c *b5/4*d - [Grünbaumian] x3/2o3/2o5/3x5/3*a5/2*c *b5/4*d - o3/2x3/2o5/3x5/3*a5/2*c *b5/4*d - [Grünbaumian] x3/2x3/2x5/3o5/3*a5/2*c *b5/4*d - [Grünbaumian] x3/2x3/2o5/3x5/3*a5/2*c *b5/4*d - [Grünbaumian] x3/2o3/2x5/3x5/3*a5/2*c *b5/4*d - [Grünbaumian] x3/2x3/2x5/3x5/3*a5/2*c *b5/4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3/2o5o3/2o5*a5/2*c *b5*d   (up)

 o3/2o5o3/2o5*a5/2*c *b5*d (µ=32) o3o5o3/2o5/4*a5/3*c *b5*d (µ=208) o3o5o3o5*a5/3*c *b5/4*d (µ=272) quasiregulars ```x3/2o5o3/2o5*a5/2*c *b5*d - (contains gacid) o3/2x5o3/2o5*a5/2*c *b5*d - (contains "2doe") ``` ```x3o5o3/2o5/4*a5/3*c *b5*d - (contains gacid) o3x5o3/2o5/4*a5/3*c *b5*d - (contains "2doe") o3o5x3/2o5/4*a5/3*c *b5*d - (contains gacid) o3o5o3/2x5/4*a5/3*c *b5*d - (contains "2doe") ``` ```x3o5o3o5*a5/3*c *b5/4*d - (contains gacid) o3x5o3o5*a5/3*c *b5/4*d - (contains "2doe") ``` otherWythoffians ```x3/2x5o3/2o5*a5/2*c *b5*d - [Grünbaumian] x3/2o5x3/2o5*a5/2*c *b5*d - [Grünbaumian] x3/2o5o3/2x5*a5/2*c *b5*d - o3/2x5o3/2x5*a5/2*c *b5*d - x3/2x5x3/2o5*a5/2*c *b5*d - [Grünbaumian] x3/2x5o3/2x5*a5/2*c *b5*d - [Grünbaumian] x3/2x5x3/2x5*a5/2*c *b5*d - [Grünbaumian] ``` ```x3x5o3/2o5/4*a5/3*c *b5*d - x3o5x3/2o5/4*a5/3*c *b5*d - x3o5o3/2x5/4*a5/3*c *b5*d - [Grünbaumian] o3x5x3/2o5/4*a5/3*c *b5*d - o3x5o3/2x5/4*a5/3*c *b5*d - o3o5x3/2x5/4*a5/3*c *b5*d - [Grünbaumian] x3x5x3/2o5/4*a5/3*c *b5*d - x3x5o3/2x5/4*a5/3*c *b5*d - [Grünbaumian] x3o5x3/2x5/4*a5/3*c *b5*d - [Grünbaumian] o3x5x3/2x5/4*a5/3*c *b5*d - [Grünbaumian] x3x5x3/2x5/4*a5/3*c *b5*d - [Grünbaumian] ``` ```x3x5o3o5*a5/3*c *b5/4*d - x3o5x3o5*a5/3*c *b5/4*d - x3o5o3x5*a5/3*c *b5/4*d - o3x5o3x5*a5/3*c *b5/4*d - [Grünbaumian] x3x5x3o5*a5/3*c *b5/4*d - x3x5o3x5*a5/3*c *b5/4*d - [Grünbaumian] x3x5x3x5*a5/3*c *b5/4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o5/4o3/2o5*a5/2*c *b5/4*d (µ=928) o3o5/4o3o5/4*a5/2*c *b5*d (µ=992) o3/2o5/4o3/2o5/4*a5/3*c *b5/4*d (µ=3632) quasiregulars ```x3o5/4o3/2o5*a5/2*c *b5/4*d - (contains gacid) o3x5/4o3/2o5*a5/2*c *b5/4*d - (contains "2doe") o3o5/4x3/2o5*a5/2*c *b5/4*d - (contains gacid) o3o5/4o3/2x5*a5/2*c *b5/4*d - (contains "2doe") ``` ```x3o5/4o3o5/4*a5/2*c *b5*d - (contains gacid) o3x5/4o3o5/4*a5/2*c *b5*d - (contains "2doe") ``` ```x3/2o5/4o3/2o5/4*a5/3*c *b5/4*d - (contains gacid) o3/2x5/4o3/2o5/4*a5/3*c *b5/4*d - (contains "2doe") ``` otherWythoffians ```x3x5/4o3/2o5*a5/2*c *b5/4*d - x3o5/4x3/2o5*a5/2*c *b5/4*d - [Grünbaumian] x3o5/4o3/2x5*a5/2*c *b5/4*d - o3x5/4x3/2o5*a5/2*c *b5/4*d - [Grünbaumian] o3x5/4o3/2x5*a5/2*c *b5/4*d - [Grünbaumian] o3o5/4x3/2x5*a5/2*c *b5/4*d - [Grünbaumian] x3x5/4x3/2o5*a5/2*c *b5/4*d - [Grünbaumian] x3x5/4o3/2x5*a5/2*c *b5/4*d - [Grünbaumian] x3o5/4x3/2x5*a5/2*c *b5/4*d - [Grünbaumian] o3x5/4x3/2x5*a5/2*c *b5/4*d - [Grünbaumian] x3x5/4x3/2x5*a5/2*c *b5/4*d - [Grünbaumian] ``` ```x3x5/4o3o5/4*a5/2*c *b5*d - x3o5/4x3o5/4*a5/2*c *b5*d - [Grünbaumian] x3o5/4o3x5/4*a5/2*c *b5*d - [Grünbaumian] o3x5/4o3x5/4*a5/2*c *b5*d - x3x5/4x3o5/4*a5/2*c *b5*d - [Grünbaumian] x3x5/4o3x5/4*a5/2*c *b5*d - [Grünbaumian] x3x5/4x3x5/4*a5/2*c *b5*d - [Grünbaumian] ``` ```x3/2x5/4o3/2o5/4*a5/3*c *b5/4*d - [Grünbaumian] x3/2o5/4x3/2o5/4*a5/3*c *b5/4*d - x3/2o5/4o3/2x5/4*a5/3*c *b5/4*d - [Grünbaumian] o3/2x5/4o3/2x5/4*a5/3*c *b5/4*d - [Grünbaumian] x3/2x5/4x3/2o5/4*a5/3*c *b5/4*d - [Grünbaumian] x3/2x5/4o3/2x5/4*a5/3*c *b5/4*d - [Grünbaumian] x3/2x5/4x3/2x5/4*a5/3*c *b5/4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5/3o3o5/3*a5*c *b5/2*d   (up)

 o3o5/3o3o5/3*a5*c *b5/2*d (µ=112) o3o5/3o3/2o5/2*a5*c *b5/3*d (µ=368) o3/2o5/2o3/2o5/2*a5*c *b5/2*d (µ=592) quasiregulars ```x3o5/3o3o5/3*a5*c *b5/2*d - (contains cid) o3x5/3o3o5/3*a5*c *b5/2*d - (contains "2gissid") ``` ```x3o5/3o3/2o5/2*a5*c *b5/3*d - (contains cid) o3x5/3o3/2o5/2*a5*c *b5/3*d - (contains "2gissid") o3o5/3x3/2o5/2*a5*c *b5/3*d - (contains cid) o3o5/3o3/2x5/2*a5*c *b5/3*d - (contains "2gissid") ``` ```x3/2o5/2o3/2o5/2*a5*c *b5/2*d - (contains cid) o3/2x5/2o3/2o5/2*a5*c *b5/2*d - (contains "2gissid") ``` otherWythoffians ```x3x5/3o3o5/3*a5*c *b5/2*d - x3o5/3x3o5/3*a5*c *b5/2*d - x3o5/3o3x5/3*a5*c *b5/2*d - o3x5/3o3x5/3*a5*c *b5/2*d - [Grünbaumian] x3x5/3x3o5/3*a5*c *b5/2*d - x3x5/3o3x5/3*a5*c *b5/2*d - [Grünbaumian] x3x5/3x3x5/3*a5*c *b5/2*d - [Grünbaumian] ``` ```x3x5/3o3/2o5/2*a5*c *b5/3*d - x3o5/3x3/2o5/2*a5*c *b5/3*d - x3o5/3o3/2x5/2*a5*c *b5/3*d - [Grünbaumian] o3x5/3x3/2o5/2*a5*c *b5/3*d - o3x5/3o3/2x5/2*a5*c *b5/3*d - o3o5/3x3/2x5/2*a5*c *b5/3*d - [Grünbaumian] x3x5/3x3/2o5/2*a5*c *b5/3*d - x3x5/3o3/2x5/2*a5*c *b5/3*d - [Grünbaumian] x3o5/3x3/2x5/2*a5*c *b5/3*d - [Grünbaumian] o3x5/3x3/2x5/2*a5*c *b5/3*d - [Grünbaumian] x3x5/3x3/2x5/2*a5*c *b5/3*d - [Grünbaumian] ``` ```x3/2x5/2o3/2o5/2*a5*c *b5/2*d - [Grünbaumian] x3/2o5/2x3/2o5/2*a5*c *b5/2*d - x3/2o5/2o3/2x5/2*a5*c *b5/2*d - [Grünbaumian] o3/2x5/2o3/2x5/2*a5*c *b5/2*d - [Grünbaumian] x3/2x5/2x3/2o5/2*a5*c *b5/2*d - [Grünbaumian] x3/2x5/2o3/2x5/2*a5*c *b5/2*d - [Grünbaumian] x3/2x5/2x3/2x5/2*a5*c *b5/2*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o5/2o3o5/2*a5/4*c *b5/3*d (µ=832) o3o5/2o3/2o5/3*a5/4*c *b5/2*d (µ=1088) o3/2o5/3o3/2o5/3*a5/4*c *b5/3*d (µ=2752) quasiregulars ```x3o5/2o3o5/2*a5/4*c *b5/3*d - (contains cid) o3x5/2o3o5/2*a5/4*c *b5/3*d - (contains "2gissid") ``` ```x3o5/2o3/2o5/3*a5/4*c *b5/2*d - (contains cid) o3x5/2o3/2o5/3*a5/4*c *b5/2*d - (contains "2gissid") o3o5/2x3/2o5/3*a5/4*c *b5/2*d - (contains cid) o3o5/2o3/2x5/3*a5/4*c *b5/2*d - (contains "2gissid") ``` ```x3/2o5/3o3/2o5/3*a5/4*c *b5/3*d - (contains cid) o3/2x5/3o3/2o5/3*a5/4*c *b5/3*d - (contains "2gissid") ``` otherWythoffians ```x3x5/2o3o5/2*a5/4*c *b5/3*d - x3o5/2x3o5/2*a5/4*c *b5/3*d - [Grünbaumian] x3o5/2o3x5/2*a5/4*c *b5/3*d - [Grünbaumian] o3x5/2o3x5/2*a5/4*c *b5/3*d - x3x5/2x3o5/2*a5/4*c *b5/3*d - [Grünbaumian] x3o5/2x3x5/2*a5/4*c *b5/3*d - [Grünbaumian] x3x5/2x3x5/2*a5/4*c *b5/3*d - [Grünbaumian] ``` ```x3x5/2o3/2o5/3*a5/4*c *b5/2*d - x3o5/2x3/2o5/3*a5/4*c *b5/2*d - [Grünbaumian] x3o5/2o3/2x5/3*a5/4*c *b5/2*d - o3x5/2x3/2o5/3*a5/4*c *b5/2*d - [Grünbaumian] o3x5/2o3/2x5/3*a5/4*c *b5/2*d - [Grünbaumian] o3o5/2x3/2x5/3*a5/4*c *b5/2*d - [Grünbaumian] x3x5/2x3/2o5/3*a5/4*c *b5/2*d - [Grünbaumian] x3x5/2o3/2x5/3*a5/4*c *b5/2*d - [Grünbaumian] x3o5/2x3/2x5/3*a5/4*c *b5/2*d - [Grünbaumian] o3x5/2x3/2x5/3*a5/4*c *b5/2*d - [Grünbaumian] x3x5/2x3/2x5/3*a5/4*c *b5/2*d - [Grünbaumian] ``` ```x3/2x5/3o3/2o5/3*a5/4*c *b5/3*d - [Grünbaumian] x3/2o5/3x3/2o5/3*a5/4*c *b5/3*d - [Grünbaumian] x3/2o5/3o3/2x5/3*a5/4*c *b5/3*d - o3/2x5/3o3/2x5/3*a5/4*c *b5/3*d - x3/2x5/3x3/2o5/3*a5/4*c *b5/3*d - [Grünbaumian] x3/2x5/3o3/2x5/3*a5/4*c *b5/3*d - [Grünbaumian] x3/2o5/3x3/2x5/3*a5/4*c *b5/3*d - [Grünbaumian] x3/2x5/3x3/2x5/3*a5/4*c *b5/3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5o5o5/3o5/3*a3/2*c *b3*d   (up)

 o5o5o5/3o5/3*a3/2*c *b3*d (µ=60) o5o5o5/2o5/2*a3/2*c *b3/2*d (µ=180) o5o5/4o5/2o5/3*a3*c *b3*d (µ=420) quasiregulars ```x5o5o5/3o5/3*a3/2*c *b3*d - o5x5o5/3o5/3*a3/2*c *b3*d - o5o5o5/3x5/3*a3/2*c *b3*d - ``` ```x5o5o5/2o5/2*a3/2*c *b3/2*d - o5x5o5/2o5/2*a3/2*c *b3/2*d - o5o5o5/2x5/2*a3/2*c *b3/2*d - ``` ```x5o5/4o5/2o5/3*a3*c *b3*d - o5x5/4o5/2o5/3*a3*c *b3*d - o5o5/4x5/2o5/3*a3*c *b3*d - o5o5/4o5/2x5/3*a3*c *b3*d - ``` otherWythoffians ```x5x5o5/3o5/3*a3/2*c *b3*d - x5o5x5/3o5/3*a3/2*c *b3*d - [Grünbaumian] x5o5o5/3x5/3*a3/2*c *b3*d - o5x5o5/3x5/3*a3/2*c *b3*d - x5x5x5/3o5/3*a3/2*c *b3*d - [Grünbaumian] x5x5o5/3x5/3*a3/2*c *b3*d - kevuthi x5o5x5/3x5/3*a3/2*c *b3*d - [Grünbaumian] x5x5x5/3x5/3*a3/2*c *b3*d - [Grünbaumian] ``` ```x5x5o5/2o5/2*a3/2*c *b3/2*d - x5o5x5/2o5/2*a3/2*c *b3/2*d - [Grünbaumian] x5o5o5/2x5/2*a3/2*c *b3/2*d - [Grünbaumian] o5x5o5/2x5/2*a3/2*c *b3/2*d - [Grünbaumian] x5x5x5/2o5/2*a3/2*c *b3/2*d - [Grünbaumian] x5x5o5/2x5/2*a3/2*c *b3/2*d - [Grünbaumian] x5o5x5/2x5/2*a3/2*c *b3/2*d - [Grünbaumian] x5x5x5/2x5/2*a3/2*c *b3/2*d - [Grünbaumian] ``` ```x5x5/4o5/2o5/3*a3*c *b3*d - x5o5/4x5/2o5/3*a3*c *b3*d - x5o5/4o5/2x5/3*a3*c *b3*d - o5x5/4x5/2o5/3*a3*c *b3*d - [Grünbaumian] o5x5/4o5/2x5/3*a3*c *b3*d - o5o5/4x5/2x5/3*a3*c *b3*d - [Grünbaumian] x5x5/4x5/2o5/3*a3*c *b3*d - [Grünbaumian] x5x5/4o5/2x5/3*a3*c *b3*d - x5o5/4x5/2x5/3*a3*c *b3*d - [Grünbaumian] o5x5/4x5/2x5/3*a3*c *b3*d - [Grünbaumian] x5x5/4x5/2x5/3*a3*c *b3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5o5/4o5/3o5/2*a3*c *b3/2*d (µ=780) o5/4o5/4o5/2o5/2*a3/2*c *b3*d (µ=1500) o5/4o5/4o5/3o5/3*a3/2*c *b3/2*d (µ=3060) quasiregulars ```x5o5/4o5/3o5/2*a3*c *b3/2*d - o5x5/4o5/3o5/2*a3*c *b3/2*d - o5o5/4x5/3o5/2*a3*c *b3/2*d - o5o5/4o5/3x5/2*a3*c *b3/2*d - ``` ```x5/4o5/4o5/2o5/2*a3/2*c *b3*d - o5/4x5/4o5/2o5/2*a3/2*c *b3*d - o5/4o5/4o5/2x5/2*a3/2*c *b3*d - ``` ```x5/4o5/4o5/3o5/3*a3/2*c *b3/2*d - o5/4x5/4o5/3o5/3*a3/2*c *b3/2*d - o5/4o5/4o5/3x5/3*a3/2*c *b3/2*d - ``` otherWythoffians ```x5x5/4o5/3o5/2*a3*c *b3/2*d - x5o5/4x5/3o5/2*a3*c *b3/2*d - x5o5/4o5/3x5/2*a3*c *b3/2*d - [Grünbaumian] o5x5/4x5/3o5/2*a3*c *b3/2*d - [Grünbaumian] o5x5/4o5/3x5/2*a3*c *b3/2*d - [Grünbaumian] o5o5/4x5/3x5/2*a3*c *b3/2*d - x5x5/4x5/3o5/2*a3*c *b3/2*d - [Grünbaumian] x5x5/4o5/3x5/2*a3*c *b3/2*d - [Grünbaumian] x5o5/4x5/3x5/2*a3*c *b3/2*d - [Grünbaumian] o5x5/4x5/3x5/2*a3*c *b3/2*d - [Grünbaumian] x5x5/4x5/3x5/2*a3*c *b3/2*d - [Grünbaumian] ``` ```x5/4x5/4o5/2o5/2*a3/2*c *b3*d - [Grünbaumian] x5/4o5/4x5/2o5/2*a3/2*c *b3*d - [Grünbaumian] x5/4o5/4o5/2x5/2*a3/2*c *b3*d - [Grünbaumian] o5/4x5/4o5/2x5/2*a3/2*c *b3*d - x5/4x5/4x5/2o5/2*a3/2*c *b3*d - [Grünbaumian] x5/4x5/4o5/2x5/2*a3/2*c *b3*d - [Grünbaumian] x5/4o5/4x5/2x5/2*a3/2*c *b3*d - [Grünbaumian] x5/4x5/4x5/2x5/2*a3/2*c *b3*d - [Grünbaumian] ``` ```x5/4x5/4o5/3o5/3*a3/2*c *b3/2*d - [Grünbaumian] x5/4o5/4x5/3o5/3*a3/2*c *b3/2*d - [Grünbaumian] x5/4o5/4o5/3x5/3*a3/2*c *b3/2*d - o5/4x5/4o5/3x5/3*a3/2*c *b3/2*d - [Grünbaumian] x5/4x5/4x5/3o5/3*a3/2*c *b3/2*d - [Grünbaumian] x5/4x5/4o5/3x5/3*a3/2*c *b3/2*d - [Grünbaumian] x5/4o5/4x5/3x5/3*a3/2*c *b3/2*d - [Grünbaumian] x5/4x5/4x5/3x5/3*a3/2*c *b3/2*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5o5o5o5*a5/4*c *b3/2*d   (up)

 o5o5o5o5*a5/4*c *b3/2*d (µ=16) o5o5/4o5/4o5*a5*c *b3/2*d (µ=224) o5o5/4o5o5/4*a5*c *b3*d (µ=496) quasiregulars ```x5o5o5o5*a5/4*c *b3/2*d - o5x5o5o5*a5/4*c *b3/2*d - ``` ```x5o5/4o5/4o5*a5*c *b3/2*d - o5x5/4o5/4o5*a5*c *b3/2*d - o5o5/4x5/4o5*a5*c *b3/2*d - ``` ```x5o5/4o5o5/4*a5*c *b3*d - o5x5/4o5o5/4*a5*c *b3*d - ``` otherWythoffians ```x5x5o5o5*a5/4*c *b3/2*d - x5o5x5o5*a5/4*c *b3/2*d - [Grünbaumian] o5x5o5x5*a5/4*c *b3/2*d - [Grünbaumian] x5x5x5o5*a5/4*c *b3/2*d - [Grünbaumian] x5x5o5x5*a5/4*c *b3/2*d - [Grünbaumian] x5x5x5x5*a5/4*c *b3/2*d - [Grünbaumian] ``` ```x5x5/4o5/4o5*a5*c *b3/2*d - x5o5/4x5/4o5*a5*c *b3/2*d - o5x5/4x5/4o5*a5*c *b3/2*d - [Grünbaumian] o5x5/4o5/4x5*a5*c *b3/2*d - [Grünbaumian] x5x5/4x5/4o5*a5*c *b3/2*d - [Grünbaumian] x5x5/4o5/4x5*a5*c *b3/2*d - [Grünbaumian] o5x5/4x5/4x5*a5*c *b3/2*d - [Grünbaumian] x5x5/4x5/4x5*a5*c *b3/2*d - [Grünbaumian] ``` ```x5x5/4o5o5/4*a5*c *b3*d - x5o5/4x5o5/4*a5*c *b3*d - x5o5/4o5x5/4*a5*c *b3*d - [Grünbaumian] o5x5/4o5x5/4*a5*c *b3*d - x5x5/4x5o5/4*a5*c *b3*d - [Grünbaumian] x5x5/4o5x5/4*a5*c *b3*d - [Grünbaumian] x5x5/4x5x5/4*a5*c *b3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5o5o5/4o5/4*a5/4*c *b3*d (µ=704) o5/4o5/4o5/4o5/4*a5/4*c *b3/2*d (µ=4336) quasiregulars ```x5o5o5/4o5/4*a5/4*c *b3*d - o5x5o5/4o5/4*a5/4*c *b3*d - o5o5o5/4x5/4*a5/4*c *b3*d - ``` ```x5/4o5/4o5/4o5/4*a5/4*c *b3/2*d - o5/4x5/4o5/4o5/4*a5/4*c *b3/2*d - ``` otherWythoffians ```x5x5o5/4o5/4*a5/4*c *b3*d - x5o5x5/4o5/4*a5/4*c *b3*d - [Grünbaumian] x5o5o5/4x5/4*a5/4*c *b3*d - [Grünbaumian] o5x5o5/4x5/4*a5/4*c *b3*d - x5x5x5/4o5/4*a5/4*c *b3*d - [Grünbaumian] x5x5o5/4x5/4*a5/4*c *b3*d - [Grünbaumian] x5o5x5/4x5/4*a5/4*c *b3*d - [Grünbaumian] x5x5x5/4x5/4*a5/4*c *b3*d - [Grünbaumian] ``` ```x5/4x5/4o5/4o5/4*a5/4*c *b3/2*d - [Grünbaumian] x5/4o5/4x5/4o5/4*a5/4*c *b3/2*d - [Grünbaumian] o5/4x5/4o5/4x5/4*a5/4*c *b3/2*d - [Grünbaumian] x5/4x5/4x5/4o5/4*a5/4*c *b3/2*d - [Grünbaumian] x5/4x5/4o5/4x5/4*a5/4*c *b3/2*d - [Grünbaumian] x5/4x5/4x5/4x5/4*a5/4*c *b3/2*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5/2o5/2o5/2o5/2*a5/2*c *b3/2*d   (up)

 o5/2o5/2o5/2o5/2*a5/2*c *b3/2*d (µ=304) o5/2o5/2o5/3o5/3*a5/2*c *b3*d (µ=416) o5/2o5/3o5/2o5/3*a5/3*c *b3*d (µ=784) quasiregulars ```x5/2o5/2o5/2o5/2*a5/2*c *b3/2*d - o5/2x5/2o5/2o5/2*a5/2*c *b3/2*d - ``` ```x5/2o5/2o5/3o5/3*a5/2*c *b3*d - o5/2x5/2o5/3o5/3*a5/2*c *b3*d - o5/2o5/2o5/3x5/3*a5/2*c *b3*d - ``` ```x5/2o5/3o5/2o5/3*a5/3*c *b3*d - o5/2x5/3o5/2o5/3*a5/3*c *b3*d - ``` otherWythoffians ```x5/2x5/2o5/2o5/2*a5/2*c *b3/2*d - [Grünbaumian] x5/2o5/2x5/2o5/2*a5/2*c *b3/2*d - [Grünbaumian] o5/2x5/2o5/2x5/2*a5/2*c *b3/2*d - [Grünbaumian] x5/2x5/2x5/2o5/2*a5/2*c *b3/2*d - [Grünbaumian] x5/2x5/2o5/2x5/2*a5/2*c *b3/2*d - [Grünbaumian] x5/2x5/2x5/2x5/2*a5/2*c *b3/2*d - [Grünbaumian] ``` ```x5/2x5/2o5/3o5/3*a5/2*c *b3*d - [Grünbaumian] x5/2o5/2x5/3o5/3*a5/2*c *b3*d - [Grünbaumian] x5/2o5/2o5/3x5/3*a5/2*c *b3*d - o5/2x5/2o5/3x5/3*a5/2*c *b3*d - x5/2x5/2x5/3o5/3*a5/2*c *b3*d - [Grünbaumian] x5/2x5/2o5/3x5/3*a5/2*c *b3*d - [Grünbaumian] x5/2o5/2x5/3x5/3*a5/2*c *b3*d - [Grünbaumian] x5/2x5/2x5/3x5/3*a5/2*c *b3*d - [Grünbaumian] ``` ```x5/2x5/3o5/2o5/3*a5/3*c *b3*d - [Grünbaumian] x5/2o5/3x5/2o5/3*a5/3*c *b3*d - x5/2o5/3o5/2x5/3*a5/3*c *b3*d - o5/2x5/3o5/2x5/3*a5/3*c *b3*d - x5/2x5/3x5/2o5/3*a5/3*c *b3*d - [Grünbaumian] x5/2x5/3o5/2x5/3*a5/3*c *b3*d - [Grünbaumian] x5/2x5/3x5/2x5/3*a5/3*c *b3*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5/2o5/3o5/3o5/2*a5/3*c *b3/2*d (µ=1376) o5/3o5/3o5/3o5/3*a5/2*c *b3/2*d (µ=1744) quasiregulars ```x5/2o5/3o5/3o5/2*a5/3*c *b3/2*d - o5/2x5/3o5/3o5/2*a5/3*c *b3/2*d - o5/2o5/3x5/3o5/2*a5/3*c *b3/2*d - ``` ```x5/3o5/3o5/3o5/3*a5/2*c *b3/2*d - o5/3x5/3o5/3o5/3*a5/2*c *b3/2*d - ``` otherWythoffians ```x5/2x5/3o5/3o5/2*a5/3*c *b3/2*d - [Grünbaumian] x5/2o5/3x5/3o5/2*a5/3*c *b3/2*d - o5/2x5/3x5/3o5/2*a5/3*c *b3/2*d - o5/2x5/3o5/3x5/2*a5/3*c *b3/2*d - [Grünbaumian] x5/2x5/3x5/3o5/2*a5/3*c *b3/2*d - [Grünbaumian] x5/2x5/3o5/3x5/2*a5/3*c *b3/2*d - [Grünbaumian] o5/2x5/3x5/3x5/2*a5/3*c *b3/2*d - [Grünbaumian] x5/2x5/3x5/3x5/2*a5/3*c *b3/2*d - [Grünbaumian] ``` ```x5/3x5/3o5/3o5/3*a5/2*c *b3/2*d - x5/3o5/3x5/3o5/3*a5/2*c *b3/2*d - [Grünbaumian] o5/3x5/3o5/3x5/3*a5/2*c *b3/2*d - [Grünbaumian] x5/3x5/3x5/3o5/3*a5/2*c *b3/2*d - [Grünbaumian] x5/3x5/3o5/3x5/3*a5/2*c *b3/2*d - [Grünbaumian] x5/3x5/3x5/3x5/3*a5/2*c *b3/2*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5o5o5o5*a5/4*c *b5/4*d   (up)

 o5o5o5o5*a5/4*c *b5/4*d (µ=264) o5o5o5/4o5/4*a5/4*c *b5*d (µ=456) o5/4o5/4o5/4o5/4*a5/4*c *b5/4*d (µ=4584) quasiregulars ```x5o5o5o5*a5/4*c *b5/4*d - ``` ```x5o5o5/4o5/4*a5/4*c *b5*d - o5x5o5/4o5/4*a5/4*c *b5*d - ``` ```x5/4o5/4o5/4o5/4*a5/4*c *b5/4*d - ``` otherWythoffians ```x5x5o5o5*a5/4*c *b5/4*d - x5o5x5o5*a5/4*c *b5/4*d - [Grünbaumian] x5x5x5o5*a5/4*c *b5/4*d - [Grünbaumian] x5x5x5x5*a5/4*c *b5/4*d - [Grünbaumian] ``` ```x5x5o5/4o5/4*a5/4*c *b5*d - x5o5x5/4o5/4*a5/4*c *b5*d - [Grünbaumian] x5x5x5/4o5/4*a5/4*c *b5*d - [Grünbaumian] x5o5x5/4x5/4*a5/4*c *b5*d - [Grünbaumian] x5x5x5/4x5/4*a5/4*c *b5*d - [Grünbaumian] ``` ```x5/4x5/4o5/4o5/4*a5/4*c *b5/4*d - [Grünbaumian] x5/4x5/4x5/4o5/4*a5/4*c *b5/4*d - [Grünbaumian] x5/4x5/4x5/4x5/4*a5/4*c *b5/4*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5/2o5/2o5/2o5/2*a5/2*c *b5/2*d   (up)

 o5/2o5/2o5/2o5/2*a5/2*c *b5/2*d (µ=24) o5/2o5/2o5/3o5/3*a5/2*c *b5/3*d (µ=696) o5/3o5/3o5/3o5/3*a5/2*c *b5/2*d (µ=1464) quasiregulars ```x5/2o5/2o5/2o5/2*a5/2*c *b5/2*d - ``` ```x5/2o5/2o5/3o5/3*a5/2*c *b5/3*d - o5/2o5/2o5/3x5/3*a5/2*c *b5/3*d - ``` ```x5/3o5/3o5/3o5/3*a5/2*c *b5/2*d - ``` otherWythoffians ```x5/2x5/2o5/2o5/2*a5/2*c *b5/2*d - [Grünbaumian] x5/2x5/2x5/2o5/2*a5/2*c *b5/2*d - [Grünbaumian] x5/2x5/2x5/2x5/2*a5/2*c *b5/2*d - [Grünbaumian] ``` ```x5/2x5/2o5/3o5/3*a5/2*c *b5/3*d - [Grünbaumian] x5/2o5/2o5/3x5/3*a5/2*c *b5/3*d - x5/2x5/2x5/3o5/3*a5/2*c *b5/3*d - [Grünbaumian] x5/2x5/2o5/3x5/3*a5/2*c *b5/3*d - [Grünbaumian] x5/2x5/2x5/3x5/3*a5/2*c *b5/3*d - [Grünbaumian] ``` ```x5/3x5/3o5/3o5/3*a5/2*c *b5/2*d - x5/3o5/3x5/3o5/3*a5/2*c *b5/2*d - [Grünbaumian] x5/3x5/3x5/3o5/3*a5/2*c *b5/2*d - [Grünbaumian] x5/3x5/3x5/3x5/3*a5/2*c *b5/2*d - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```