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---- 4D ----

This page is available sorted by point-group symmetry (below)
or by complexity (only including[[:space:]]starry[[:space:]]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



  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-
Simplical Dynkin Graphs Others
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



linear ones
o-P-o-Q-o-R-o

Pentachoral ("pentic") Symmetries   (up)

  o3o3o3o (convex) o3o3o3/2o (µ=4) o3o3/2o3o (µ=6)
quasiregulars
x3o3o3o - pen
o3x3o3o - rap
x3o3o3/2o - pen
o3x3o3/2o - rap
o3o3x3/2o - rap
o3o3o3/2x - pen
x3o3/2o3o - pen
o3x3/2o3o - rap
other
Wythoffians
x3x3o3o - tip
x3o3x3o - srip
x3o3o3x - spid
o3x3x3o - deca
x3x3x3o - grip
x3x3o3x - prip
x3x3x3x - gippid
x3x3o3/2o - tip
x3o3x3/2o - srip
x3o3o3/2x - 2firp
o3x3x3/2o - deca
o3x3o3/2x - pinnip+5 2thah
o3o3x3/2x - 4pen
x3x3x3/2o - grip
x3x3o3/2x - pirpop+5 2thah
x3o3x3/2x - [Grünbaumian]
o3x3x3/2x - sirdop+10{6/2}
x3x3x3/2x - [Grünbaumian]
x3x3/2o3o - tip
x3o3/2x3o - pinnip+5 2thah
x3o3/2o3x - 2firp
o3x3/2x3o - 6pen
x3x3/2x3o - [Grünbaumian]
x3x3/2o3x - pirpop+5 2thah
x3x3/2x3x - 2garpop+20{6/2}
(partial)
snubs and
holosnubs
β3o3o3o - 3pen
o3β3o3o - firp+rap+15{4}
β3x3o3o - 2rap
x3β3o3o - (?) *)
β3β3o3o - 2rap+20tet
β3o3x3o - rawvtip
x3o3β3o - pinnipdip+15{4}
β3o3β3o - (?) *)
β3o3o3x - piphid+10tet
β3o3o3β - 4pen+160{3}
o3β3x3o - (?) *)
o3β3β3o - (?) *)
β3x3x3o - 2deca
x3β3x3o - 2srip
x3x3β3o - (?) *)
β3β3x3o - 2srip
β3x3β3o - (?) *)
x3β3β3o - 2srip+20trip
β3β3β3o - (?) *)
β3x3o3x - 2srip
x3β3o3x - (?) *)
x3x3o3β - pittip
β3β3o3x - 2srip+20{6}+40{3} **)
β3x3o3β - 2srip+20{6}+60{3} **)
x3β3o3β - (?) *)
β3β3o3β - (?) *)
β3x3x3x - 2grip
x3β3x3x - 2prip
β3β3x3x - 2prip
β3x3β3x - (?) *)
β3x3x3β - (?) *)
x3β3β3x - (?) *)
β3β3β3x - (?) *)
β3β3x3β - (?) *)
s3s3s3s - snip *)
...
...
  o3o3/2o3/2o (µ=9) o3/2o3o3/2o (µ=11) o3/2o3/2o3/2o (µ=16)
quasiregulars
x3o3/2o3/2o - pen
o3x3/2o3/2o - rap
o3o3/2x3/2o - rap
o3o3/2o3/2x - pen
x3/2o3o3/2o - pen
o3/2x3o3/2o - rap
x3/2o3/2o3/2o - pen
o3/2x3/2o3/2o - rap
other
Wythoffians
x3x3/2o3/2o - tip
x3o3/2x3/2o - pinnip+5 2thah
x3o3/2o3/2x - spid
o3x3/2x3/2o - 6pen
o3x3/2o3/2x - srip
o3o3/2x3/2x - 4pen
x3x3/2x3/2o - [Grünbaumian]
x3x3/2o3/2x - prip
x3o3/2x3/2x - [Grünbaumian]
o3x3/2x3/2x - [Grünbaumian]
x3x3/2x3/2x - [Grünbaumian]
x3/2x3o3/2o - 4pen
x3/2o3x3/2o - pinnip+5 2thah
x3/2o3o3/2x - spid
o3/2x3x3/2o - deca
x3/2x3x3/2o - sirdop+10{6/2}
x3/2x3o3/2x - [Grünbaumian]
x3/2x3x3/2x - [Grünbaumian]
x3/2x3/2o3/2o - 4pen
x3/2o3/2x3/2o - srip
x3/2o3/2o3/2x - 2firp
o3/2x3/2x3/2o - 6pen
x3/2x3/2x3/2o - [Grünbaumian]
x3/2x3/2o3/2x - [Grünbaumian]
x3/2x3/2x3/2x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...


Tesseractic ("tessic") Symmetries   (up)

  o3o3o4o (convex) o3/2o3o4o (µ=7) o3o3o4/3o (µ=15) o3o3/2o4o (µ=17)
quasiregulars
x3o3o4o - hex
o3x3o4o - ico
o3o3x4o - rit
o3o3o4x - tes
x3/2o3o4o - hex
o3/2x3o4o - ico
o3/2o3x4o - rit
o3/2o3o4x - tes
x3o3o4/3o - hex
o3x3o4/3o - ico
o3o3x4/3o - rit
o3o3o4/3x - tes
x3o3/2o4o - hex
o3x3/2o4o - ico
o3o3/2x4o - rit
o3o3/2o4x - tes
other
Wythoffians
x3x3o4o - thex
x3o3x4o - rico
x3o3o4x - sidpith
o3x3x4o - tah
o3x3o4x - srit
o3o3x4x - tat
x3x3x4o - tico
x3x3o4x - prit
x3o3x4x - proh
o3x3x4x - grit
x3x3x4x - gidpith
x3/2x3o4o - [Grünbaumian]
x3/2o3x4o - 2huhoh+3tes+8co
x3/2o3o4x - quidpith
o3/2x3x4o - tah
o3/2x3o4x - srit
o3/2o3x4x - tat
x3/2x3x4o - [Grünbaumian]
x3/2x3o4x - [Grünbaumian]
x3/2o3x4x - spript+16 2thah
o3/2x3x4x - grit
x3/2x3x4x - [Grünbaumian]
x3x3o4/3o - thex
x3o3x4/3o - rico
x3o3o4/3x - quidpith
o3x3x4/3o - tah
o3x3o4/3x - qrit
o3o3x4/3x - quitit
x3x3x4/3o - tico
x3x3o4/3x - paqrit
x3o3x4/3x - quiproh
o3x3x4/3x - gaqrit
x3x3x4/3x - gaquidpoth
x3x3/2o4o - thex
x3o3/2x4o - 2huhoh+3tes+8co
x3o3/2o4x - quidpith
o3x3/2x4o - [Grünbaumian]
o3x3/2o4x - qrit
o3o3/2x4x - tat
x3x3/2x4o - [Grünbaumian]
x3x3/2o4x - paqrit
x3o3/2x4x - spript+16 2thah
o3x3/2x4x - [Grünbaumian]
x3x3/2x4x - [Grünbaumian]
(partial)
snubs and
holosnubs
β3o3o4o - 2hex+8oct
o3β3o4o - ico+gico+72{4}
o3o3β4o - (?) *)
o3o3o4s - hex
o3o3o4β - haddet
β3x3o4o - 2ico
x3β3o4o - (?) *)
β3β3o4o - 2ico+48{4}+128{3} **)
β3o3x4o - rawvhitto
x3o3β4o - (?) *)
β3o3β4o - (?) *)
β3o3o4x - shafipto+32tet
β3o3o4β - (?) *)
x3o3o4s - rit
o3β3x4o - (?) *)
o3x3β4o - (?) *)
o3β3β4o - (?) *)
o3β3o4x - pinpith+48{4}
o3x3o4s - thex
o3β3o4β - (?) *)
o3o3β4x - (?) *)
o3o3x4s - rit
o3o3β4β - 2rit+64tet
β3x3x4o - 2tah
x3β3x4o - 2rico
x3x3β4o - (?) *)
β3β3x4o - 2rico
β3x3β4o - (?) *)
x3β3β4o - (?) *)
s3s3s4o - sadi
β3x3o4x - 2srit
x3β3o4x - (?) *)
x3x3o4s - tah
β3β3o4x - 2srit+48{8}+128{3} **)
β3x3o4β - (?) *)
x3β3o4β - (?) *)
β3β3o4β - (?) *)
β3o3x4x - siphado
x3o3β4x - (?) *)
x3o3x4s - rico
β3o3β4x - (?) *)
β3o3x4β - 2rico+64{6}+192{3} **)
x3o3β4β - 2rico+64{6}+128{3} **)
β3o3β4β - (?) *)
o3β3x4x - (?) *)
o3x3β4x - 2srit
o3x3x4s - tah
o3β3β4x - 2srit+64trip
o3β3x4β - (?) *)
o3x3β4β - 2srit
o3β3β4β - (?) *)
β3x3x4x - 2grit
x3β3x4x - 2proh
x3x3β4x - 2prit
x3x3x4s - tico
β3β3x4x - 2proh
β3x3β4x - (?) *)
β3x3x4β - (?) *)
x3β3β4x - (?) *)
x3β3x4β - (?) *)
x3x3β4β - 2prit
s3s3s4x - (?) *)
β3β3x4β - (?) *)
β3x3β4β - (?) *)
x3β3β4β - (?) *)
s3s3s4s - snet *)
...
...
...
  o3/2o3/2o4o (µ=23) o3o3/2o4/3o (µ=31) o3/2o3o4/3o (µ=41) o3/2o3/2o4/3o (µ=57)
quasiregulars
x3/2o3/2o4o - hex
o3/2x3/2o4o - ico
o3/2o3/2x4o - rit
o3/2o3/2o4x - tes
x3o3/2o4/3o - hex
o3x3/2o4/3o - ico
o3o3/2x4/3o - rit
o3o3/2o4/3x - tes
x3/2o3o4/3o - hex
o3/2x3o4/3o - ico
o3/2o3x4/3o - rit
o3/2o3o4/3x - tes
x3/2o3/2o4/3o - hex
o3/2x3/2o4/3o - ico
o3/2o3/2x4/3o - rit
o3/2o3/2o4/3x - tes
other
Wythoffians
x3/2x3/2o4o - [Grünbaumian]
x3/2o3/2x4o - rico
x3/2o3/2o4x - sidpith
o3/2x3/2x4o - [Grünbaumian]
o3/2x3/2o4x - qrit
o3/2o3/2x4x - tat
x3/2x3/2x4o - [Grünbaumian]
x3/2x3/2o4x - [Grünbaumian]
x3/2o3/2x4x - proh
o3/2x3/2x4x - [Grünbaumian]
x3/2x3/2x4x - [Grünbaumian]
x3x3/2o4/3o - thex
x3o3/2x4/3o - 2huhoh+3tes+8co
x3o3/2o4/3x - sidpith
o3x3/2x4/3o - [Grünbaumian]
o3x3/2o4/3x - srit
o3o3/2x4/3x - quitit
x3x3/2x4/3o - [Grünbaumian]
x3x3/2o4/3x - prit
x3o3/2x4/3x - gapript+16 2thah
o3x3/2x4/3x - [Grünbaumian]
x3x3/2x4/3x - [Grünbaumian]
x3/2x3o4/3o - [Grünbaumian]
x3/2o3x4/3o - 2huhoh+3tes+8co
x3/2o3o4/3x - sidpith
o3/2x3x4/3o - tah
o3/2x3o4/3x - qrit
o3/2o3x4/3x - quitit
x3/2x3x4/3o - [Grünbaumian]
x3/2x3o4/3x - [Grünbaumian]
x3/2o3x4/3x - gapript+16 2thah
o3/2x3x4/3x - gaqrit
x3/2x3x4/3x - [Grünbaumian]
x3/2x3/2o4/3o - [Grünbaumian]
x3/2o3/2x4/3o - rico
x3/2o3/2o4/3x - quidpith
o3/2x3/2x4/3o - [Grünbaumian]
o3/2x3/2o4/3x - srit
o3/2o3/2x4/3x - quitit
x3/2x3/2x4/3o - [Grünbaumian]
x3/2x3/2o4/3x - [Grünbaumian]
x3/2o3/2x4/3x - quiproh
o3/2x3/2x4/3x - [Grünbaumian]
x3/2x3/2x4/3x - [Grünbaumian]
(partial)
snubs and
holosnubs
s3/2s3/2s4o - rasdi
...
...
...
...


Icositetrachoral ("icoic") Symmetries   (up)

  o3o4o3o (convex) o3o4o3/2o (µ=23) o3o4/3o3o (µ=73)
quasiregulars
x3o4o3o - ico
o3x4o3o - rico
x3o4o3/2o - ico
o3x4o3/2o - rico
o3o4x3/2o - rico
o3o4o3/2x - ico
x3o4/3o3o - ico
o3x4/3o3o - rico
other
Wythoffians
x3x4o3o - tico
x3o4x3o - srico
x3o4o3x - spic
o3x4x3o - cont
x3x4x3o - grico
x3x4o3x - prico
x3x4x3x - gippic
x3x4o3/2o - tico
x3o4x3/2o - srico
x3o4o3/2x - quippic
o3x4x3/2o - cont
o3x4o3/2x - qrico
o3o4x3/2x - [Grünbaumian]
x3x4x3/2o - grico
x3x4o3/2x - paqri
x3o4x3/2x - [Grünbaumian]
o3x4x3/2x - [Grünbaumian]
x3x4x3/2x - [Grünbaumian]
x3x4/3o3o - tico
x3o4/3x3o - qrico
x3o4/3o3x - quippic
o3x4/3x3o - gic
x3x4/3x3o - gaqri
x3x4/3o3x - paqri
x3x4/3x3x - gaquapac
(partial)
snubs and
holosnubs
β3o4o3o - ico+gico+72{4}
o3β4o3o - (?) *)
β3x4o3o - 2rico
x3β4o3o - (?) *)
s3s4o3o - sadi
β3o4x3o - rawvaty
x3o4β3o - (?) *)
β3o4β3o - (?) *)
β3o4o3x - inpac+72{4}
β3o4o3β - (?) *)
o3β4x3o - (?) *)
o3β4β3o - (?) *)
β3x4x3o - 2cont
x3β4x3o - 2srico
x3x4β3o - (?) *)
s3s4x3o - srico
β3x4β3o - (?) *)
x3β4β3o - 2srico+192trip
β3β4β3o - (?) *)
β3x4o3x - 2srico
x3β4o3x - (?) *)
x3x4o3β - sipti
s3s4o3x - prissi **)
β3x4o3β - 2srico+144{8}+576{3} **)
x3β4o3β - (?) *)
β3β4o3β - (?) *)
β3x4x3x - 2grico
x3β4x3x - 2prico
s3s4x3x - prico
β3x4β3x - (?) *)
β3x4x3β - (?) *)
x3β4β3x - (?) *)
β3β4β3x - (?) *)
β3β4x3β - (?) *)
s3s4s3s - snico *)
o3o4s3/2s - rasdi
x3o4s3/2s - prarsi **)
...
...
  o3o4/3o3/2o (µ=95) o3/2o4o3/2o (µ=97) o3/2o4/3o3/2o (µ=169)
quasiregulars
x3o4/3o3/2o - ico
o3x4/3o3/2o - rico
o3o4/3x3/2o - rico
o3o4/3o3/2x - ico
x3/2o4o3/2o - ico
o3/2x4o3/2o - rico
x3/2o4/3o3/2o - ico
o3/2x4/3o3/2o - rico
other
Wythoffians
x3x4/3o3/2o - tico
x3o4/3x3/2o - qrico
x3o4/3o3/2x - spic
o3x4/3x3/2o - gic
o3x4/3o3/2x - srico
o3o4/3x3/2x - [Grünbaumian]
x3x4/3x3/2o - gaqri
x3x4/3o3/2x - prico
x3o4/3x3/2x - [Grünbaumian]
o3x4/3x3/2x - [Grünbaumian]
x3x4/3x3/2x - [Grünbaumian]
x3/2x4o3/2o - [Grünbaumian]
x3/2o4x3/2o - qrico
x3/2o4o3/2x - spic
o3/2x4x3/2o - cont
x3/2x4x3/2o - [Grünbaumian]
x3/2x4o3/2x - [Grünbaumian]
x3/2x4x3/2x - [Grünbaumian]
x3/2x4/3o3/2o - [Grünbaumian]
x3/2o4/3x3/2o - srico
x3/2o4/3o3/2x - quippic
o3/2x4/3x3/2o - gic
x3/2x4/3x3/2o - [Grünbaumian]
x3/2x4/3o3/2x - [Grünbaumian]
x3/2x4/3x3/2x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...


Hecatonicosachoral ("hyic") Symmetries – type o3o3o5o   (up)

  o3o3o5o (convex) o3/2o3o5o (µ=119) o3o3o5/4o (µ=599) o3o3/2o5o (µ=601)
quasiregulars
x3o3o5o - ex
o3x3o5o - rox
o3o3x5o - rahi
o3o3o5x - hi
x3/2o3o5o - ex
o3/2x3o5o - rox
o3/2o3x5o - rahi
o3/2o3o5x - hi
x3o3o5/4o - ex
o3x3o5/4o - rox
o3o3x5/4o - rahi
o3o3o5/4x - hi
x3o3/2o5o - ex
o3x3/2o5o - rox
o3o3/2x5o - rahi
o3o3/2o5x - hi
other
Wythoffians
x3x3o5o - tex
x3o3x5o - srix
x3o3o5x - sidpixhi
o3x3x5o - xhi
o3x3o5x - srahi
o3o3x5x - thi
x3x3x5o - grix
x3x3o5x - prahi
x3o3x5x - prix
o3x3x5x - grahi
x3x3x5x - gidpixhi
x3/2x3o5o - 3ex+fix
x3/2o3x5o - frox+600 2thah
x3/2o3o5x - saquid paxhi
o3/2x3x5o - xhi
o3/2x3o5x - srahi
o3/2o3x5x - thi
x3/2x3x5o - [Grünbaumian]
x3/2x3o5x - [Grünbaumian]
x3/2o3x5x - spriphi+600 2thah
o3/2x3x5x - grahi
x3/2x3x5x - [Grünbaumian]
x3x3o5/4o - tex
x3o3x5/4o - srix
x3o3o5/4x - saquid paxhi
o3x3x5/4o - xhi
o3x3o5/4x - (contains gicdatrid)
o3o3x5/4x - [Grünbaumian]
x3x3x5/4o - grix
x3x3o5/4x - (contains gicdatrid)
x3o3x5/4x - [Grünbaumian]
o3x3x5/4x - [Grünbaumian]
x3x3x5/4x - [Grünbaumian]
x3x3/2o5o - tex
x3o3/2x5o - frox+600 2thah
x3o3/2o5x - saquid paxhi
o3x3/2x5o - 3ex+2fix+gaghi
o3x3/2o5x - (contains gicdatrid)
o3o3/2x5x - thi
x3x3/2x5o - [Grünbaumian]
x3x3/2o5x - (contains gicdatrid)
x3o3/2x5x - spriphi+600 2thah
o3x3/2x5x - [Grünbaumian]
x3x3/2x5x - [Grünbaumian]
(partial)
snubs and
holosnubs
β3o3o5o - 2ex+120ike
o3β3o5o - rox+720pip
o3o3β5o - (?) *)
o3o3o5β - sidtaxhi
β3x3o5o - 2rox
x3β3o5o - (?) *)
β3β3o5o - 2rox+1440{5}+2400{3} **)
β3o3x5o - srawv hixhi
x3o3β5o - (?) *)
β3o3β5o - (?) *)
β3o3o5x - six fipady+1200tet
x3o3o5β - stut phiddix
β3o3o5β - (?) *)
o3β3x5o - (?) *)
o3x3β5o - (?) *)
o3β3β5o - (?) *)
o3β3o5x - pinpixhi+1800{4}
o3x3o5β - wavhiddix
o3β3o5β - (?) *)
o3o3β5x - (?) *)
o3o3x5β - 2rahi
o3o3β5β - 2rahi+2400tet
β3x3x5o - 2xhi
x3β3x5o - 2srix
x3x3β5o - (?) *)
β3β3x5o - 2srix
β3x3β5o - (?) *)
x3β3β5o - (?) *)
β3β3β5o - (?) *)
β3x3o5x - 2srahi
x3β3o5x - (?) *)
x3x3o5β - sphiddix
β3β3o5x - 2srahi+1440{10}+4800{3} **)
β3x3o5β - (?) *)
x3β3o5β - (?) *)
β3β3o5β - (?) *)
β3o3x5x - spixhihy
x3o3β5x - (?) *)
x3o3x5β - 2srix
β3o3β5x - (?) *)
β3o3x5β - 2srix+2400{6}+7200{3} **)
x3o3β5β - 2srix+2400{6}+4800{3} **)
β3o3β5β - (?) *)
o3β3x5x - (?) *)
o3x3β5x - 2srahi
o3x3x5β - 2xhi
o3β3β5x - 2srahi+2400trip
o3β3x5β - (?) *)
o3x3β5β - 2srahi
o3β3β5β - (?) *)
β3x3x5x - 2grahi
x3β3x5x - 2prix
x3x3β5x - 2prahi
x3x3x5β - 2grix
β3β3x5x - 2prix
β3x3β5x - (?) *)
β3x3x5β - (?) *)
x3β3β5x - (?) *)
x3β3x5β - (?) *)
x3x3β5β - 2prahi
β3β3β5x - (?) *)
β3β3x5β - (?) *)
β3x3β5β - (?) *)
x3β3β5β - (?) *)
s3s3s5s - snixhi *)
...
...
...
  o3/2o3/2o5o (µ=719) o3o3/2o5/4o (µ=1199) o3/2o3o5/4o (µ=1681) o3/2o3/2o5/4o (µ=2281)
quasiregulars
x3/2o3/2o5o - ex
o3/2x3/2o5o - rox
o3/2o3/2x5o - rahi
o3/2o3/2o5x - hi
x3o3/2o5/4o - ex
o3x3/2o5/4o - rox
o3o3/2x5/4o - rahi
o3o3/2o5/4x - hi
x3/2o3o5/4o - ex
o3/2x3o5/4o - rox
o3/2o3x5/4o - rahi
o3/2o3o5/4x - hi
x3/2o3/2o5/4o - ex
o3/2x3/2o5/4o - rox
o3/2o3/2x5/4o - rahi
o3/2o3/2o5/4x - hi
other
Wythoffians
x3/2x3/2o5o - 3ex+fix
x3/2o3/2x5o - srix
x3/2o3/2o5x - sidpixhi
o3/2x3/2x5o - 3ex+2fix+gaghi
o3/2x3/2o5x - (contains gicdatrid)
o3/2o3/2x5x - thi
x3/2x3/2x5o - 2rox+sophi
x3/2x3/2o5x - [Grünbaumian]
x3/2o3/2x5x - prix
o3/2x3/2x5x - [Grünbaumian]
x3/2x3/2x5x - [Grünbaumian]
x3x3/2o5/4o - tex
x3o3/2x5/4o - frox+600 2thah
x3o3/2o5/4x - sidpixhi
o3x3/2x5/4o - 3ex+2fix+gaghi
o3x3/2o5/4x - srahi
o3o3/2x5/4x - [Grünbaumian]
x3x3/2x5/4o - [Grünbaumian]
x3x3/2o5/4x - prahi
x3o3/2x5/4x - [Grünbaumian]
o3x3/2x5/4x - [Grünbaumian]
x3x3/2x5/4x - [Grünbaumian]
x3/2x3o5/4o - 3ex+fix
x3/2o3x5/4o - frox+600 2thah
x3/2o3o5/4x - sidpixhi
o3/2x3x5/4o - xhi
o3/2x3o5/4x - (contains gicdatrid)
o3/2o3x5/4x - [Grünbaumian]
x3/2x3x5/4o - [Grünbaumian]
x3/2x3o5/4x - [Grünbaumian]
x3/2o3x5/4x - [Grünbaumian]
o3/2x3x5/4x - [Grünbaumian]
x3/2x3x5/4x - [Grünbaumian]
x3/2x3/2o5/4o - 3ex+fix
x3/2o3/2x5/4o - srix
x3/2o3/2o5/4x - saquid paxhi
o3/2x3/2x5/4o - 3ex+2fix+gaghi
o3/2x3/2o5/4x - srahi
o3/2o3/2x5/4x - [Grünbaumian]
x3/2x3/2x5/4o - 2rox+sophi
x3/2x3/2o5/4x - [Grünbaumian]
x3/2o3/2x5/4x - [Grünbaumian]
o3/2x3/2x5/4x - [Grünbaumian]
x3/2x3/2x5/4x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...
...


Hecatonicosachoral ("hyic") Symmetries – type o3o3o5/2o   (up)

  o3o3o5/2o (µ=191) o3o3o5/3o (µ=409) o3/2o3o5/2o (µ=649) o3o3/2o5/2o (µ=791)
quasiregulars
x3o3o5/2o - gax
o3x3o5/2o - raggix
o3o3x5/2o - rigogishi
o3o3o5/2x - gogishi
x3o3o5/3o - gax
o3x3o5/3o - raggix
o3o3x5/3o - rigogishi
o3o3o5/3x - gogishi
x3/2o3o5/2o - gax
o3/2x3o5/2o - raggix
o3/2o3x5/2o - rigogishi
o3/2o3o5/2x - gogishi
x3o3/2o5/2o - gax
o3x3/2o5/2o - raggix
o3o3/2x5/2o - rigogishi
o3o3/2o5/2x - gogishi
other
Wythoffians
x3x3o5/2o - taggix
x3o3x5/2o - sirgax
x3o3o5/2x - quad pagaxhi
o3x3x5/2o - gixhi
o3x3o5/2x - (contains sicdatrid)
o3o3x5/2x - [Grünbaumian]
x3x3x5/2o - graggix
x3x3o5/2x - (contains sicdatrid)
x3o3x5/2x - [Grünbaumian]
o3x3x5/2x - [Grünbaumian]
x3x3x5/2x - [Grünbaumian]
x3x3o5/3o - taggix
x3o3x5/3o - sirgax
x3o3o5/3x - quidpixhi
o3x3x5/3o - gixhi
o3x3o5/3x - qrigogishi
            (old: qrahi)
o3o3x5/3x - quit gogishi
x3x3x5/3o - graggix
x3x3o5/3x - paqrigagishi
            (old: paqrahi)
x3o3x5/3x - quippirgax
o3x3x5/3x - gaqrigagishi
x3x3x5/3x - gaquidapixhi
x3/2x3o5/2o - [Grünbaumian]
x3/2o3x5/2o - ripahi+600 2thah
x3/2o3o5/2x - quidpixhi
o3/2x3x5/2o - gixhi
o3/2x3o5/2x - (contains sicdatrid)
o3/2o3x5/2x - [Grünbaumian]
x3/2x3x5/2o - [Grünbaumian]
x3/2x3o5/2x - [Grünbaumian]
x3/2o3x5/2x - [Grünbaumian]
o3/2x3x5/2x - [Grünbaumian]
x3/2x3x5/2x - [Grünbaumian]
x3x3/2o5/2o - taggix
x3o3/2x5/2o - ripahi+600 2thah
x3o3/2o5/2x - quidpixhi
o3x3/2x5/2o - [Grünbaumian]
o3x3/2o5/2x - qrigogishi
              (old: qrahi)
o3o3/2x5/2x - [Grünbaumian]
x3x3/2x5/2o - [Grünbaumian]
x3x3/2o5/2x - paqrigagishi
              (old: paqrahi)
x3o3/2x5/2x - [Grünbaumian]
o3x3/2x5/2x - [Grünbaumian]
x3x3/2x5/2x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...
...
  o3o3/2o5/3o (µ=1009) o3/2o3o5/3o (µ=1151) o3/2o3/2o5/2o (µ=1249) o3/2o3/2o5/3o (µ=1751)
quasiregulars
x3o3/2o5/3o - gax
o3x3/2o5/3o - raggix
o3o3/2x5/3o - rigogishi
o3o3/2o5/3x - gogishi
x3/2o3o5/3o - gax
o3/2x3o5/3o - raggix
o3/2o3x5/3o - rigogishi
o3/2o3o5/3x - gogishi
x3/2o3/2o5/2o - gax
o3/2x3/2o5/2o - raggix
o3/2o3/2x5/2o - rigogishi
o3/2o3/2o5/2x - gogishi
x3/2o3/2o5/3o - gax
o3/2x3/2o5/3o - raggix
o3/2o3/2x5/3o - rigogishi
o3/2o3/2o5/3x - gogishi
other
Wythoffians
x3x3/2o5/3o - taggix
x3o3/2x5/3o - ripahi+600 2thah
x3o3/2o5/3x - quad pagaxhi
o3x3/2x5/3o - [Grünbaumian]
o3x3/2o5/3x - (contains sicdatrid)
o3o3/2x5/3x - quit gogishi
x3x3/2x5/3o - [Grünbaumian]
x3x3/2o5/3x - (contains sicdatrid)
x3o3/2x5/3x - gipriphi+600 2thah
o3x3/2x5/3x - [Grünbaumian]
x3x3/2x5/3x - [Grünbaumian]
x3/2x3o5/3o - [Grünbaumian]
x3/2o3x5/3o - ripahi+600 2thah
x3/2o3o5/3x - quad pagaxhi
o3/2x3x5/3o - gixhi
o3/2x3o5/3x - qrigogishi
              (old: qrahi)
o3/2o3x5/3x - quit gogishi
x3/2x3x5/3o - [Grünbaumian]
x3/2x3o5/3x - [Grünbaumian]
x3/2o3x5/3x - gipriphi+600 2thah
o3/2x3x5/3x - gaqrigagishi
x3/2x3x5/3x - [Grünbaumian]
x3/2x3/2o5/2o - [Grünbaumian]
x3/2o3/2x5/2o - sirgax
x3/2o3/2o5/2x - quad pagaxhi
o3/2x3/2x5/2o - [Grünbaumian]
o3/2x3/2o5/2x - qrigogishi
                (old: qrahi)
o3/2o3/2x5/2x - [Grünbaumian]
x3/2x3/2x5/2o - [Grünbaumian]
x3/2x3/2o5/2x - [Grünbaumian]
x3/2o3/2x5/2x - [Grünbaumian]
o3/2x3/2x5/2x - [Grünbaumian]
x3/2x3/2x5/2x - [Grünbaumian]
x3/2x3/2o5/3o - [Grünbaumian]
x3/2o3/2x5/3o - sirgax
x3/2o3/2o5/3x - quidpixhi
o3/2x3/2x5/3o - [Grünbaumian]
o3/2x3/2o5/3x - (contains sicdatrid)
o3/2o3/2x5/3x - quit gogishi
x3/2x3/2x5/3o - [Grünbaumian]
x3/2x3/2o5/3x - [Grünbaumian]
x3/2o3/2x5/3x - quippirgax
o3/2x3/2x5/3x - [Grünbaumian]
x3/2x3/2x5/3x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...
...


Hecatonicosachoral ("hyic") Symmetries – type o3o5o5/2o   (up)

  o3o5o5/2o (µ=4) o3o5o5/3o (µ=116) o3/2o5o5/2o (µ=356) o3/2o5o5/3o (µ=964)
quasiregulars
x3o5o5/2o - fix
o3x5o5/2o - rofix
o3o5x5/2o - rasishi
o3o5o5/2x - sishi
x3o5o5/3o - fix
o3x5o5/3o - rofix
o3o5x5/3o - rasishi
o3o5o5/3x - sishi
x3/2o5o5/2o - fix
o3/2x5o5/2o - rofix
o3/2o5x5/2o - rasishi
o3/2o5o5/2x - sishi
x3/2o5o5/3o - fix
o3/2x5o5/3o - rofix
o3/2o5x5/3o - rasishi
o3/2o5o5/3x - sishi
other
Wythoffians
x3x5o5/2o - tiffix
x3o5x5/2o - sirfix
x3o5o5/2x - padohi
o3x5x5/2o - shihi
o3x5o5/2x - sirsashi
o3o5x5/2x - [Grünbaumian]
x3x5x5/2o - girfix
x3x5o5/2x - pirshi
x3o5x5/2x - [Grünbaumian]
o3x5x5/2x - [Grünbaumian]
x3x5x5/2x - [Grünbaumian]
x3x5o5/3o - tiffix
x3o5x5/3o - sirfix
x3o5o5/3x - sishi+paphicki+gridaphi
o3x5x5/3o - shihi
o3x5o5/3x - (contains cadditradid)
o3o5x5/3x - quit sishi
x3x5x5/3o - girfix
x3x5o5/3x - (contains cadditradid)
x3o5x5/3x - quippirfix
o3x5x5/3x - gaqrisashi
x3x5x5/3x - goquidipdy
x3/2x5o5/2o - [Grünbaumian]
x3/2o5x5/2o - (contains gicdatrid)
x3/2o5o5/2x - sishi+paphicki+gridaphi
o3/2x5x5/2o - shihi
o3/2x5o5/2x - sirsashi
o3/2o5x5/2x - [Grünbaumian]
x3/2x5x5/2o - [Grünbaumian]
x3/2x5o5/2x - [Grünbaumian]
x3/2o5x5/2x - [Grünbaumian]
o3/2x5x5/2x - [Grünbaumian]
x3/2x5x5/2x - [Grünbaumian]
x3/2x5o5/3o - [Grünbaumian]
x3/2o5x5/3o - (contains gicdatrid)
x3/2o5o5/3x - padohi
o3/2x5x5/3o - shihi
o3/2x5o5/3x - (contains cadditradid)
o3/2o5x5/3x - quit sishi
x3/2x5x5/3o - [Grünbaumian]
x3/2x5o5/3x - [Grünbaumian]
x3/2o5x5/3x - (contains gicdatrid)
o3/2x5x5/3x - gaqrisashi
x3/2x5x5/3x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...
...
  o3o5/4o5/2o (µ=1084) o3o5/4o5/3o (µ=1196) o3/2o5/4o5/2o (µ=1436) o3/2o5/4o5/3o (µ=2044)
quasiregulars
x3o5/4o5/2o - fix
o3x5/4o5/2o - rofix
o3o5/4x5/2o - rasishi
o3o5/4o5/2x - sishi
x3o5/4o5/3o - fix
o3x5/4o5/3o - rofix
o3o5/4x5/3o - rasishi
o3o5/4o5/3x - sishi
x3/2o5/4o5/2o - fix
o3/2x5/4o5/2o - rofix
o3/2o5/4x5/2o - rasishi
o3/2o5/4o5/2x - sishi
x3/2o5/4o5/3o - fix
o3/2x5/4o5/3o - rofix
o3/2o5/4x5/3o - rasishi
o3/2o5/4o5/3x - sishi
other
Wythoffians
x3x5/4o5/2o - tiffix
x3o5/4x5/2o - (contains gicdatrid)
x3o5/4o5/2x - sishi+paphicki+gridaphi
o3x5/4x5/2o - [Grünbaumian]
o3x5/4o5/2x - (contains cadditradid)
o3o5/4x5/2x - [Grünbaumian]
x3x5/4x5/2o - [Grünbaumian]
x3x5/4o5/2x - (contains cadditradid)
x3o5/4x5/2x - [Grünbaumian]
o3x5/4x5/2x - [Grünbaumian]
x3x5/4x5/2x - [Grünbaumian]
x3x5/4o5/3o - tiffix
x3o5/4x5/3o - (contains gicdatrid)
x3o5/4o5/3x - padohi
o3x5/4x5/3o - [Grünbaumian]
o3x5/4o5/3x - sirsashi
o3o5/4x5/3x - quit sishi
x3x5/4x5/3o - [Grünbaumian]
x3x5/4o5/3x - pirshi
x3o5/4x5/3x - (contains gicdatrid)
o3x5/4x5/3x - [Grünbaumian]
x3x5/4x5/3x - [Grünbaumian]
x3/2x5/4o5/2o - [Grünbaumian]
x3/2o5/4x5/2o - sirfix
x3/2o5/4o5/2x - padohi
o3/2x5/4x5/2o - [Grünbaumian]
o3/2x5/4o5/2x - (contains cadditradid)
o3/2o5/4x5/2x - [Grünbaumian]
x3/2x5/4x5/2o - [Grünbaumian]
x3/2x5/4o5/2x - [Grünbaumian]
x3/2o5/4x5/2x - [Grünbaumian]
o3/2x5/4x5/2x - [Grünbaumian]
x3/2x5/4x5/2x - [Grünbaumian]
x3/2x5/4o5/3o - [Grünbaumian]
x3/2o5/4x5/3o - sirfix
x3/2o5/4o5/3x - sishi+paphicki+gridaphi
o3/2x5/4x5/3o - [Grünbaumian]
o3/2x5/4o5/3x - sirsashi
o3/2o5/4x5/3x - quit sishi
x3/2x5/4x5/3o - [Grünbaumian]
x3/2x5/4o5/3x - [Grünbaumian]
x3/2o5/4x5/3x - quippirfix
o3/2x5/4x5/3x - [Grünbaumian]
x3/2x5/4x5/3x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...
...


Hecatonicosachoral ("hyic") Symmetries – type o3o5/2o5o   (up)

  o3o5/2o5o (µ=76) o3/2o5/2o5o (µ=284) o3o5/3o5o (µ=436) o3/2o5/3o5o (µ=644)
quasiregulars
x3o5/2o5o - gofix
o3x5/2o5o - rigfix
o3o5/2x5o - ragaghi
o3o5/2o5x - gaghi
x3/2o5/2o5o - gofix
o3/2x5/2o5o - rigfix
o3/2o5/2x5o - ragaghi
o3/2o5/2o5x - gaghi
x3o5/3o5o - gofix
o3x5/3o5o - rigfix
o3o5/3x5o - ragaghi
o3o5/3o5x - gaghi
x3/2o5/3o5o - gofix
o3/2x5/3o5o - rigfix
o3/2o5/3x5o - ragaghi
o3/2o5/3o5x - gaghi
other
Wythoffians
x3x5/2o5o - tigfix
x3o5/2x5o - (contains sicdatrid)
x3o5/2o5x - quipdohi
o3x5/2x5o - [Grünbaumian]
o3x5/2o5x - sirgaghi
o3o5/2x5x - tigaghi
x3x5/2x5o - [Grünbaumian]
x3x5/2o5x - pirgaghi
x3o5/2x5x - (contains sicdatrid)
o3x5/2x5x - [Grünbaumian]
x3x5/2x5x - [Grünbaumian]
x3/2x5/2o5o - [Grünbaumian]
x3/2o5/2x5o - qrigfix
              (old: querfix)
x3/2o5/2o5x - gaghi+paphacki+sridaphi
o3/2x5/2x5o - [Grünbaumian]
o3/2x5/2o5x - sirgaghi
o3/2o5/2x5x - tigaghi
x3/2x5/2x5o - [Grünbaumian]
x3/2x5/2o5x - [Grünbaumian]
x3/2o5/2x5x - paqrigafix
              (old: paquerfix)
o3/2x5/2x5x - [Grünbaumian]
x3/2x5/2x5x - [Grünbaumian]
x3x5/3o5o - tigfix
x3o5/3x5o - qrigfix
            (old: querfix)
x3o5/3o5x - gaghi+paphacki+sridaphi
o3x5/3x5o - ghihi
o3x5/3o5x - (contains cadditradid)
o3o5/3x5x - tigaghi
x3x5/3x5o - gaqrigafix
x3x5/3o5x - (contains cadditradid)
x3o5/3x5x - paqrigafix
            (old: paquerfix)
o3x5/3x5x - gaqrigaghi
x3x5/3x5x - gaquidipdy
x3/2x5/3o5o - [Grünbaumian]
x3/2o5/3x5o - (contains sicdatrid)
x3/2o5/3o5x - quipdohi
o3/2x5/3x5o - ghihi
o3/2x5/3o5x - (contains cadditradid)
o3/2o5/3x5x - tigaghi
x3/2x5/3x5o - [Grünbaumian]
x3/2x5/3o5x - [Grünbaumian]
x3/2o5/3x5x - (contains sicdatrid)
o3/2x5/3x5x - gaqrigaghi
x3/2x5/3x5x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...
...
  o3o5/2o5/4o (µ=764) o3o5/3o5/4o (µ=1124) o3/2o5/2o5/4o (µ=1756) o3/2o5/3o5/4o (µ=2116)
quasiregulars
x3o5/2o5/4o - gofix
o3x5/2o5/4o - rigfix
o3o5/2x5/4o - ragaghi
o3o5/2o5/4x - gaghi
x3o5/3o5/4o - gofix
o3x5/3o5/4o - rigfix
o3o5/3x5/4o - ragaghi
o3o5/3o5/4x - gaghi
x3/2o5/2o5/4o - gofix
o3/2x5/2o5/4o - rigfix
o3/2o5/2x5/4o - ragaghi
o3/2o5/2o5/4x - gaghi
x3/2o5/3o5/4o - gofix
o3/2x5/3o5/4o - rigfix
o3/2o5/3x5/4o - ragaghi
o3/2o5/3o5/4x - gaghi
other
Wythoffians
x3x5/2o5/4o - tigfix
x3o5/2x5/4o - (contains sicdatrid)
x3o5/2o5/4x - gaghi+paphacki+sridaphi
o3x5/2x5/4o - [Grünbaumian]
o3x5/2o5/4x - (contains cadditradid)
o3o5/2x5/4x - [Grünbaumian]
x3x5/2x5/4o - [Grünbaumian]
x3x5/2o5/4x - (contains cadditradid)
x3o5/2x5/4x - [Grünbaumian]
o3x5/2x5/4x - [Grünbaumian]
x3x5/2x5/4x - [Grünbaumian]
x3x5/3o5/4o - tigfix
x3o5/3x5/4o - qrigfix
              (old: querfix)
x3o5/3o5/4x - quipdohi
o3x5/3x5/4o - ghihi
o3x5/3o5/4x - sirgaghi
o3o5/3x5/4x - [Grünbaumian]
x3x5/3x5/4o - gaqrigafix
x3x5/3o5/4x - pirgaghi
x3o5/3x5/4x - [Grünbaumian]
o3x5/3x5/4x - [Grünbaumian]
x3x5/3x5/4x - [Grünbaumian]
x3/2x5/2o5/4o - [Grünbaumian]
x3/2o5/2x5/4o - qrigfix
                (old: querfix)
x3/2o5/2o5/4x - quipdohi
o3/2x5/2x5/4o - [Grünbaumian]
o3/2x5/2o5/4x - (contains cadditradid)
o3/2o5/2x5/4x - [Grünbaumian]
x3/2x5/2x5/4o - [Grünbaumian]
x3/2x5/2o5/4x - [Grünbaumian]
x3/2o5/2x5/4x - [Grünbaumian]
o3/2x5/2x5/4x - [Grünbaumian]
x3/2x5/2x5/4x - [Grünbaumian]
x3/2x5/3o5/4o - [Grünbaumian]
x3/2o5/3x5/4o - (contains sicdatrid)
x3/2o5/3o5/4x - gaghi+paphacki+sridaphi
o3/2x5/3x5/4o - ghihi
o3/2x5/3o5/4x - sirgaghi
o3/2o5/3x5/4x - [Grünbaumian]
x3/2x5/3x5/4o - [Grünbaumian]
x3/2x5/3o5/4x - [Grünbaumian]
x3/2o5/3x5/4x - [Grünbaumian]
o3/2x5/3x5/4x - [Grünbaumian]
x3/2x5/3x5/4x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...
...


Hecatonicosachoral ("hyic") Symmetries – type o5o3o5/2o   (up)

  o5o3o5/2o (µ=20) o5o3o5/3o (µ=100) o5o3/2o5/2o (µ=620) o5o3/2o5/3o (µ=700)
quasiregulars
x5o3o5/2o - gahi
o5x3o5/2o - raghi
o5o3x5/2o - ragishi
o5o3o5/2x - gishi
x5o3o5/3o - gahi
o5x3o5/3o - raghi
o5o3x5/3o - ragishi
o5o3o5/3x - gishi
x5o3/2o5/2o - gahi
o5x3/2o5/2o - raghi
o5o3/2x5/2o - ragishi
o5o3/2o5/2x - gishi
x5o3/2o5/3o - gahi
o5x3/2o5/3o - raghi
o5o3/2x5/3o - ragishi
o5o3/2o5/3x - gishi
other
Wythoffians
x5x3o5/2o - taghi
x5o3x5/2o - sraghi
x5o3o5/2x - siddapady
o5x3x5/2o - dahi
o5x3o5/2x - (contains sicdatrid)
o5o3x5/2x - [Grünbaumian]
x5x3x5/2o - graghi
x5x3o5/2x - (contains sicdatrid)
x5o3x5/2x - [Grünbaumian]
o5x3x5/2x - [Grünbaumian]
x5x3x5/2x - [Grünbaumian]
x5x3o5/3o - taghi
x5o3x5/3o - sraghi
x5o3o5/3x - quadippady
o5x3x5/3o - dahi
o5x3o5/3x - qragishi
            (old: qraghi)
o5o3x5/3x - quit gishi
x5x3x5/3o - graghi
x5x3o5/3x - paqrigshi
            (old: paqraghi)
x5o3x5/3x - quippirghi
o5x3x5/3x - gaqrigashi
x5x3x5/3x - gaquidphihi
x5x3/2o5/2o - taghi
x5o3/2x5/2o - (contains gicdatrid)
x5o3/2o5/2x - quadippady
o5x3/2x5/2o - [Grünbaumian]
o5x3/2o5/2x - qragishi
              (old: qraghi)
o5o3/2x5/2x - [Grünbaumian]
x5x3/2x5/2o - [Grünbaumian]
x5x3/2o5/2x - paqrigshi
              (old: paqraghi)
x5o3/2x5/2x - [Grünbaumian]
o5x3/2x5/2x - [Grünbaumian]
x5x3/2x5/2x - [Grünbaumian]
x5x3/2o5/3o - taghi
x5o3/2x5/3o - (contains gicdatrid)
x5o3/2o5/3x - siddapady
o5x3/2x5/3o - [Grünbaumian]
o5x3/2o5/3x - (contains sicdatrid)
o5o3/2x5/3x - quit gishi
x5x3/2x5/3o - [Grünbaumian]
x5x3/2o5/3x - (contains sicdatrid)
x5o3/2x5/3x - (contains gicdatrid)
o5x3/2x5/3x - [Grünbaumian]
x5x3/2x5/3x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...
...
  o5/4o3o5/2o (µ=820) o5/4o3/2o5/2o (µ=1420) o5/4o3o5/3o (µ=1460) o5/4o3/2o5/3o (µ=2060)
quasiregulars
x5/4o3o5/2o - gahi
o5/4x3o5/2o - raghi
o5/4o3x5/2o - ragishi
o5/4o3o5/2x - gishi
x5/4o3/2o5/2o - gahi
o5/4x3/2o5/2o - raghi
o5/4o3/2x5/2o - ragishi
o5/4o3/2o5/2x - gishi
x5/4o3o5/3o - gahi
o5/4x3o5/3o - raghi
o5/4o3x5/3o - ragishi
o5/4o3o5/3x - gishi
x5/4o3/2o5/3o - gahi
o5/4x3/2o5/3o - raghi
o5/4o3/2x5/3o - ragishi
o5/4o3/2o5/3x - gishi
other
Wythoffians
x5/4x3o5/2o - [Grünbaumian]
x5/4o3x5/2o - (contains gicdatrid)
x5/4o3o5/2x - quadippady
o5/4x3x5/2o - dahi
o5/4x3o5/2x - (contains sicdatrid)
o5/4o3x5/2x - [Grünbaumian]
x5/4x3x5/2o - [Grünbaumian]
x5/4x3o5/2x - [Grünbaumian]
x5/4o3x5/2x - [Grünbaumian]
o5/4x3x5/2x - [Grünbaumian]
x5/4x3x5/2x - [Grünbaumian]
x5/4x3/2o5/2o - [Grünbaumian]
x5/4o3/2x5/2o - sraghi
x5/4o3/2o5/2x - siddapady
o5/4x3/2x5/2o - [Grünbaumian]
o5/4x3/2o5/2x - qragishi
                (old: qraghi)
o5/4o3/2x5/2x - [Grünbaumian]
x5/4x3/2x5/2o - [Grünbaumian]
x5/4x3/2o5/2x - [Grünbaumian]
x5/4o3/2x5/2x - [Grünbaumian]
o5/4x3/2x5/2x - [Grünbaumian]
x5/4x3/2x5/2x - [Grünbaumian]
x5/4x3o5/3o - [Grünbaumian]
x5/4o3x5/3o - (contains gicdatrid)
x5/4o3o5/3x - siddapady
o5/4x3x5/3o - dahi
o5/4x3o5/3x - qragishi
              (old: qraghi)
o5/4o3x5/3x - quit gishi
x5/4x3x5/3o - [Grünbaumian]
x5/4x3o5/3x - [Grünbaumian]
x5/4o3x5/3x - (contains gicdatrid)
o5/4x3x5/3x - gaqrigashi
x5/4x3x5/3x - [Grünbaumian]
x5/4x3/2o5/3o - [Grünbaumian]
x5/4o3/2x5/3o - sraghi
x5/4o3/2o5/3x - quadippady
o5/4x3/2x5/3o - [Grünbaumian]
o5/4x3/2o5/3x - (contains sicdatrid)
o5/4o3/2x5/3x - quit gishi
x5/4x3/2x5/3o - [Grünbaumian]
x5/4x3/2o5/3x - [Grünbaumian]
x5/4o3/2x5/3x - quippirghi
o5/4x3/2x5/3x - [Grünbaumian]
x5/4x3/2x5/3x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...
...


Hecatonicosachoral ("hyic") Symmetries – type o5o5/2o5o   (up)

  o5o5/2o5o (µ=6) o5o5/2o5/4o (µ=354) o5o5/3o5o (µ=366)
quasiregulars
x5o5/2o5o - gohi
o5x5/2o5o - righi
x5o5/2o5/4o - gohi
o5x5/2o5/4o - righi
o5o5/2x5/4o - righi
o5o5/2o5/4x - gohi
x5o5/3o5o - gohi
o5x5/3o5o - righi
other
Wythoffians
x5x5/2o5o - tighi
x5o5/2x5o - sirghi
x5o5/2o5x - 2sophi
o5x5/2x5o - [Grünbaumian]
x5x5/2x5o - [Grünbaumian]
x5x5/2o5x - pirghi
x5x5/2x5x - [Grünbaumian]
x5x5/2o5/4o - tighi
x5o5/2x5/4o - sirghi
x5o5/2o5/4x - 2gaghi+2paphacki
o5x5/2x5/4o - [Grünbaumian]
o5x5/2o5/4x - (contains cadditradid)
o5o5/2x5/4x - [Grünbaumian]
x5x5/2x5/4o - [Grünbaumian]
x5x5/2o5/4x - (contains cadditradid)
x5o5/2x5/4x - [Grünbaumian]
o5x5/2x5/4x - [Grünbaumian]
x5x5/2x5/4x - [Grünbaumian]
x5x5/3o5o - tighi
x5o5/3x5o - (contains cadditradid)
x5o5/3o5x - 2gaghi+2paphacki
o5x5/3x5o - 2gitphi
x5x5/3x5o - gaqrigohi
x5x5/3o5x - (contains cadditradid)
x5x5/3x5x - 2gidditpix+2dithix
(partial)
snubs and
holosnubs
β5o5/2o5o - 3sishi
β5o5/2o5x - sidpippady+120sissid
...
...
...
  o5o5/3o5/4o (µ=714) o5/4o5/2o5/4o (µ=2166) o5/4o5/3o5/4o (µ=2526)
quasiregulars
x5o5/3o5/4o - gohi
o5x5/3o5/4o - righi
o5o5/3x5/4o - righi
o5o5/3o5/4x - gohi
x5/4o5/2o5/4o - gohi
o5/4x5/2o5/4o - righi
x5/4o5/3o5/4o - gohi
o5/4x5/3o5/4o - righi
other
Wythoffians
x5x5/3o5/4o - tighi
x5o5/3x5/4o - (contains cadditradid)
x5o5/3o5/4x - 2sophi
o5x5/3x5/4o - 2gitphi
o5x5/3o5/4x - sirghi
o5o5/3x5/4x - [Grünbaumian]
x5x5/3x5/4o - gaqrigohi
x5x5/3o5/4x - pirghi
x5o5/3x5/4x - [Grünbaumian]
o5x5/3x5/4x - [Grünbaumian]
x5x5/3x5/4x - [Grünbaumian]
x5/4x5/2o5/4o - [Grünbaumian]
x5/4o5/2x5/4o - (contains cadditradid)
x5/4o5/2o5/4x - 2sophi
o5/4x5/2x5/4o - [Grünbaumian]
x5/4x5/2x5/4o - [Grünbaumian]
x5/4x5/2o5/4x - [Grünbaumian]
x5/4x5/2x5/4x - [Grünbaumian]
x5/4x5/3o5/4o - [Grünbaumian]
x5/4o5/3x5/4o - sirghi
x5/4o5/3o5/4x - 2gaghi+2paphacki
o5/4x5/3x5/4o - 2gitphi
x5/4x5/3x5/4o - [Grünbaumian]
x5/4x5/3o5/4x - [Grünbaumian]
x5/4x5/3x5/4x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...


Hecatonicosachoral ("hyic") Symmetries – type o5/2o5o5/2o   (up)

  o5/2o5o5/2o (µ=66) o5/2o5o5/3o (µ=294) o5/3o5o5/3o (µ=786)
quasiregulars
x5/2o5o5/2o - gashi
o5/2x5o5/2o - ragashi
x5/2o5o5/3o - gashi
o5/2x5o5/3o - ragashi
o5/2o5x5/3o - ragashi
o5/2o5o5/3x - gashi
x5/3o5o5/3o - gashi
o5/3x5o5/3o - ragashi
other
Wythoffians
x5/2x5o5/2o - [Grünbaumian]
x5/2o5x5/2o - sirgashi
x5/2o5o5/2x - 2sishi+2paphicki
o5/2x5x5/2o - 2sitphi
x5/2x5x5/2o - [Grünbaumian]
x5/2x5o5/2x - [Grünbaumian]
x5/2x5x5/2x - [Grünbaumian]
x5/2x5o5/3o - [Grünbaumian]
x5/2o5x5/3o - sirgashi
x5/2o5o5/3x - 2quiphi
o5/2x5x5/3o - 2sitphi
o5/2x5o5/3x - (contains cadditradid)
o5/2o5x5/3x - quit gashi
x5/2x5x5/3o - [Grünbaumian]
x5/2x5o5/3x - [Grünbaumian]
x5/2o5x5/3x - quippirgashi
o5/2x5x5/3x - giqragashi
x5/2x5x5/3x - [Grünbaumian]
x5/3x5o5/3o - quit gashi
x5/3o5x5/3o - (contains cadditradid)
x5/3o5o5/3x - 2sishi+2paphicki
o5/3x5x5/3o - 2sitphi
x5/3x5x5/3o - giqragashi
x5/3x5o5/3x - (contains cadditradid)
x5/3x5x5/3x - 2sidditpix+2dithix
(partial)
snubs and
holosnubs
...
...
...
  o5/2o5/4o5/2o (µ=1146) o5/2o5/4o5/3o (µ=1374) o5/3o5/4o5/3o (µ=1866)
quasiregulars
x5/2o5/4o5/2o - gashi
o5/2x5/4o5/2o - ragashi
x5/2o5/4o5/3o - gashi
o5/2x5/4o5/3o - ragashi
o5/2o5/4x5/3o - ragashi
o5/2o5/4o5/3x - gashi
x5/3o5/4o5/3o - gashi
o5/3x5/4o5/3o - ragashi
other
Wythoffians
x5/2x5/4o5/2o - [Grünbaumian]
x5/2o5/4x5/2o - (contains cadditradid)
x5/2o5/4o5/2x - 2quiphi
o5/2x5/4x5/2o - [Grünbaumian]
x5/2x5/4x5/2o - [Grünbaumian]
x5/2x5/4o5/2x - [Grünbaumian]
x5/2x5/4x5/2x - [Grünbaumian]
x5/2x5/4o5/3o - [Grünbaumian]
x5/2o5/4x5/3o - (contains cadditradid)
x5/2o5/4o5/3x - 2sishi+2paphicki
o5/2x5/4x5/3o - [Grünbaumian]
o5/2x5/4o5/3x - sirgashi
o5/2o5/4x5/3x - quit gashi
x5/2x5/4x5/3o - [Grünbaumian]
x5/2x5/4o5/3x - [Grünbaumian]
x5/2o5/4x5/3x - (contains cadditradid)
o5/2x5/4x5/3x - [Grünbaumian]
x5/2x5/4x5/3x - [Grünbaumian]
x5/3x5/4o5/3o - quit gashi
x5/3o5/4x5/3o - sirgashi
x5/3o5/4o5/3x - 2quiphi
o5/3x5/4x5/3o - [Grünbaumian]
x5/3x5/4x5/3o - [Grünbaumian]
x5/3x5/4o5/3x - quippirgashi
x5/3x5/4x5/3x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...


tridental ones
o-P-o-Q-o *b-R-o   =

  o_
     -P_
         >o---R---o  
     _Q-
  o-

Demitesseractic ("demitessic") Symmetries   (up)

  o3o3o *b3o (convex) o3o3o *b3/2o (µ=7) o3/2o3/2o *b3o (µ=17) o3/2o3/2o *b3/2o (µ=23)
quasiregulars
x3o3o *b3o - hex
o3x3o *b3o - ico
x3o3o *b3/2o - hex
o3x3o *b3/2o - ico
o3o3o *b3/2x - hex
x3/2o3/2o *b3o - hex
o3/2x3/2o *b3o - ico
o3/2o3/2o *b3x - hex
x3/2o3/2o *b3/2o - hex
o3/2x3/2o *b3/2o - ico
other
Wythoffians
x3x3o *b3o - thex
x3o3x *b3o - rit
x3x3x *b3o - tah
x3o3x *b3x - rico
x3x3x *b3x - tico
x3x3o *b3/2o - thex
x3o3x *b3/2o - rit
x3o3o *b3/2x - 2tho+24{4}
o3x3o *b3/2x - [Grünbaumian]
x3x3x *b3/2o - tah
x3x3o *b3/2x - [Grünbaumian]
x3o3x *b3/2x - gico+8co+16 2thah
x3x3x *b3/2x - [Grünbaumian]
x3/2x3/2o *b3o - [Grünbaumian]
x3/2o3/2x *b3o - rit
x3/2o3/2o *b3x - 2tho+24{4}
o3/2x3/2o *b3x - thex
x3/2x3/2x *b3o - [Grünbaumian]
x3/2x3/2o *b3x - [Grünbaumian]
x3/2o3/2x *b3x - gico+8co+16 2thah
x3/2x3/2x *b3x - [Grünbaumian]
x3/2x3/2o *b3/2o - [Grünbaumian]
x3/2o3/2x *b3/2o - rit
x3/2x3/2x *b3/2o - [Grünbaumian]
x3/2o3/2x *b3/2x - rico
x3/2x3/2x *b3/2x - [Grünbaumian]
(partial)
snubs and
holosnubs
β3o3o *b3o - 2hex+8oct
o3β3o *b3o - ico+gico+72{4}
β3x3o *b3o - 2ico
x3β3o *b3o - (?) *)
β3β3o *b3o - 2ico+48{4}+128{3} **)
β3o3x *b3o - sto+16tet
β3o3β *b3o - (?) *)
β3x3x *b3o - 2thex
x3β3x *b3o - (?) *)
β3β3x *b3o - (?) *)
β3x3β *b3o - (?) *)
β3β3β *b3o - (?) *)
β3o3x *b3x - rawvhitto
β3o3β *b3x - (?) *)
β3o3β *b3β - (?) *)
β3x3x *b3x - 2tah
x3β3x *b3x - 2rico
β3β3x *b3x - 2rico
β3x3β *b3x - (?) *)
β3β3β *b3x - (?) *)
β3x3β *b3β - (?) *)
s3s3s *b3s - sadi
...
...
s3/2s3/2s *b3/2s - rasdi
...


(Multi-) Prism Symmetries   (up)


Tetrahedral Prism Symmetries   (up)

  o o3o3o (convex) o o3/2o3o3*b (µ=2) o o3/2o3o (µ=3)
quasiregular
components
x x3o3o - tepe
x o3x3o - ope
x x3/2o3o3*b - (contains "2tet")
x o3/2o3x3*b - (contains "2tet")
x x3/2o3o - tepe
x o3/2x3o - ope
x o3/2o3x - tepe
other
Wythoffians
x x3x3o - tuttip
x x3o3x - cope
x x3x3x - tope
x x3/2x3o3*b - (contains "2oct")
x x3/2o3x3*b - ohope
x x3/2x3x3*b - (contains "2tut")
x x3/2x3o - (contains "3tet")
x x3/2o3x - 2thahp
x o3/2x3x - tuttip
x x3/2x3x - (contains "cho+4{6/2}")
(partial)
snubs and
holosnubs
x2s3s3s - ipe
x s3s3s - ipe
s2s3s3s - snittap *)
...
...
...
  o o3/2o3/2o (µ=5) o o3/2o3/2o3/2*b (µ=6)  
quasiregular
components
x x3/2o3/2o - tepe
x o3/2x3/2o - ope
x x3/2o3/2o3/2*b - (contains "2tet")
 
other
Wythoffians
x x3/2x3/2o - (contains "3tet")
x x3/2o3/2x - cope
x x3/2x3/2x - (contains "2oct+6{4}")
x x3/2x3/2o3/2*b - (contains "2oct")
x x3/2x3/2x3/2*b - (contains "6tet")
 
(partial)
snubs and
holosnubs
x s3/2s3/2s - gipe
...
...
 


Octahedral Prism Symmetries   (up)

  o o3o4o (convex) o o3/2o4o4*b (µ=2) o o4/3o3o4*b (µ=4) o o3/2o4o (µ=5)
quasiregular
components
x x3o4o - ope
x o3x4o - cope
x o3o4x - tes
x x3/2o4o4*b - (contains "oct+6{4}")
x o3/2o4x4*b - (contains "2cube")
x x4/3o3o4*b - (contains "2cube")
x o4/3x3o4*b - (contains "oct+6{4}")
x o4/3o3x4*b - (contains "oct+6{4}")
x x3/2o4o - ope
x o3/2x4o - cope
x o3/2o4x - tes
other
Wythoffians
x x3x4o - tope
x x3o4x - sircope
x o3x4x - ticcup
x x3x4x - gircope
x x3/2x4o4*b - (contains "2co")
x x3/2o4x4*b - soccope
x x3/2x4x4*b - (contains "2tic")
x x4/3x3o4*b - goccope
x x4/3o3x4*b - soccope
x o4/3x3x4*b - (contains "2cho")
x x4/3x3x4*b - cotcope
x x3/2x4o - (contains "2oct+6{4}")
x x3/2o4x - quercope
x o3/2x4x - ticcup
x x3/2x4x - (contains "sroh+8{6/2}")
(partial)
snubs and
holosnubs
x2o3o4s - tepe
x o3o4s - tepe
s2o3o4s - hex
x2s3s4o - ipe
x s3s4o - ipe
s2s3s4o - snittap *)
s2s3s4x - pysna *)
s2x3o4s - tuta
s2o3x4s - cope
s2x3x4s - tope
x2s3s4x - sircope
x s3s4x - sircope
x s3s4s - sniccup
s2s3s4s - sniccap *)
...
...
...
x s3/2s4o - gipe
...
  o o4/3o3o (µ=7) o o4/3o3/2o (µ=11) o o4/3o4/3o3/2*a (µ=14)  
quasiregular
components
x x4/3o3o - tes
x o4/3x3o - cope
x o4/3o3x - ope
x x4/3o3/2o - tes
x o4/3x3/2o - cope
x o4/3o3/2x - ope
x x4/3o4/3o3/2*b - (contains "oct+6{4}")
x o4/3x4/3o3/2*b - (contains "2cube")
 
other
Wythoffians
x x4/3x3o - quithip
x x4/3o3x - quercope
x o4/3x3x - tope
x x4/3x3x - quitcope
x x4/3x3/2o - quithip
x x4/3o3/2x - sircope
x o4/3x3/2x - (contains "2oct+6{4}")
x x4/3x3/2x - (contains "groh+8{6/2}")
x x4/3x4/3o3/2*b - goccope
x x4/3o4/3x3/2*b - (contains "2co")
x x4/3x4/3x3/2*b - (contains "2quith")
 
(partial)
snubs and
holosnubs
x o4/3s3s - ipe
...
x o4/3s3/2s - gipe
...
...
 


Icosahedral Prism Symmetries   (up)

  o o3o5o (convex) o o5/2o3o3*b (µ=2) o o3/2o5o5*b (µ=2)
quasiregular
components
x x3o5o - ipe
x o3x5o - iddip
x o3o5x - dope
x x5/2o3o3*b - sidtiddip
x o5/2o3x3*b - (contains "2ike")
x x3/2o5o5*b - (contains cid)
x o3/2o5x5*b - (contains "2doe")
other
Wythoffians
x x3x5o - tipe
x x3o5x - sriddip
x o3x5x - tiddip
x x3x5x - griddip
x x5/2x3o3*b - (contains "2id")
x x5/2o3x3*b - siidip
x x5/2x3x3*b - (contains "2ti")
x x3/2x5o5*b - (contains "2id")
x x3/2o5x5*b - saddiddip
x x3/2x5x5*b - (contains "2tid")
(partial)
snubs and
holosnubs
x s3s5s - sniddip
β2o3o5β - sidtidap
β2x3o5β - siida
s2s3s5s - sniddap *)
...
x s5/2s3s3*a - sesidip
...
...
  o o5/2o5o (µ=3) o o5/3o3o5*b (µ=4) o o5/2o5/2o5/2*b (µ=6)
quasiregular
components
x x5/2o5o - sissiddip
x o5/2x5o - diddip
x o5/2o5x - gaddip
x x5/3o3o5*b - ditdiddip
x o5/3x3o5*b - (contains gacid)
x o5/3o3x5*b - (contains cid)
x x5/2o5/2o5/2*b - (contains "2sissid")
other
Wythoffians
x x5/2x5o - (contains "3doe")
x x5/2o5x - radiddip
x o5/2x5x - tigiddip
x x5/2x5x - (contains "sird+12{10/2}")
x x5/3x3o5*b - gidditdiddip
x x5/3o3x5*b - sidditdiddip
x o5/3x3x5*b - ididdip
x x5/3x3x5*b - idtiddip
x x5/2x5/2o5/2*b - (contains "2did")
x x5/2x5/2x5/2*b - (contains "6doe")
(partial)
snubs and
holosnubs
x s5/2s5s - siddiddip
β2o5/2o5β - "hossdap+2 2sissid"
...
x s5/3s3s5*b - sididdip
...
...
  o o3/2o3o5*b (µ=6) o o5/4o5o5*b (µ=6) o o5/2o3o (µ=7)
quasiregular
components
x x3/2o3o5*b - gidtiddip
x o3/2x3o5*b - (contains "2gike")
x o3/2o3x5*b - gidtiddip
x x5/4o5o5*b - (contains "2gad")
x o5/4o5x5*b - (contains "2gad")
x x5/2o3o - gissiddip
x o5/2x3o - giddip
x o5/2o3x - gipe
other
Wythoffians
x x3/2x3o5*b - (contains "3ike+gad")
x x3/2o3x5*b - (contains "2seihid")
x o3/2x3x5*b - giidip
x x3/2x3x5*b - (contains "siddy+20{6/2}")
x x5/4x5o5*b - (contains "2did")
x x5/4o5x5*b - (contains "2sidhid")
x x5/4x5x5*b - (contains "2tigid")
x x5/2x3o - (contains "2gad+ike")
x x5/2o3x - (contains sicdatrid)
x o5/2x3x - tiggipe
x x5/2x3x - (contains "ri+12{10/2}")
(partial)
snubs and
holosnubs
...
...
x s5/2s3s - gosiddip
β2β5/2o3o - gidtidap
...
  o o3/2o5/2o5*b (µ=8) o o5/3o5o (µ=9) o o5/4o3o5*b (µ=10)
quasiregular
components
x x3/2o5/2o5*b - (contains cid)
x o3/2x5/2o5*b - (contains gacid)
x o3/2o5/2x5*b - ditdiddip
x x5/3o5o - sissiddip
x o5/3x5o - diddip
x o5/3o5x - gaddip
x x5/4o3o5*b - (contains "2doe")
x o5/4x3o5*b - (contains cid)
x o5/4o3x5*b - (contains cid)
other
Wythoffians
x x3/2x5/2o5*b - (contains "sidtid+gidtid")
x x3/2o5/2x5*b - sidditdiddip
x o3/2x5/2x5*b - (contains "ike+3gad")
x x3/2x5/2x5*b - (contains "id+seihid+sidhid")
x x5/3x5o - quit sissiddip
x x5/3o5x - (contains cadditradid)
x o5/3x5x - tigiddip
x x5/3x5x - quitdiddip
x x5/4x3o5*b - (contains "sidtid+ditdid")
x x5/4o3x5*b - saddiddip
x o5/4x3x5*b - (contains "2gidhei")
x x5/4x3x5*b - (contains "siddy+12{10/4}")
(partial)
snubs and
holosnubs
...
x s5/3s5s - isdiddip
...
...
  o o5/3o5/2o3*b (µ=10) o o3/2o5o (µ=11) o o5/3o3o (µ=13)
quasiregular
components
x x5/3o5/2o3*b - (contains gacid)
x o5/3x5/2o3*b - (contains "2gissid")
x o5/3o5/2x3*b - (contains gacid)
x x3/2o5o - ipe
x o3/2x5o - iddip
x o3/2o5x - dope
x x5/3o3o - gissiddip
x o5/3x3o - giddip
x o5/3o3x - gipe
other
Wythoffians
x x5/3x5/2o3*b - gaddiddip
x x5/3o5/2x3*b - (contains "2sidhei")
x o5/3x5/2x3*b - (contains "ditdid+gidtid")
x x5/3x5/2x3*b - (contains "giddy+12{10/2}")
x x3/2x5o - (contains "2ike+gad")
x x3/2o5x - (contains gicdatrid)
x o3/2x5x - tiddip
x x3/2x5x - (contains "sird+20{6/2}")
x x5/3x3o - quit gissiddip
x x5/3o3x - qriddip
x o5/3x3x - tiggipe
x x5/3x3x - gaquatiddip
(partial)
snubs and
holosnubs
x s5/3s5/2s3*b - gisdiddip
...
...
x s5/3s3s - gisiddip
...
  o o5/4o3o3*b (µ=14) o o3/2o5/2o5/2*b (µ=14) o o5/4o5/2o3*b (µ=16)
quasiregular
components
x x5/4o3o3*b - gidtiddip
x o5/4o3x3*b - (contains "2gike")
x x3/2o5/2o5/2*b - (contains gacid)
x o3/2o5/2x5/2*b - (contains "2gissid")
x x5/4o5/2o3*b - (contains cid)
x o5/4x5/2o3*b - ditdiddip
x o5/4o5/2x3*b - (contains gacid)
other
Wythoffians
x x5/4x3o3*b - (contains "2gid")
x x5/4o3x3*b - giidip
x x5/4x3x3*b - (contains "2tiggy")
x x3/2x5/2o5/2*b - (contains "2gid")
x x3/2o5/2x5/2*b - (contains "ditdid+gidtid")
x x3/2x5/2x5/2*b - (contains "2ike+4gad")
x x5/4x5/2o3*b - (contains "3sissid+gike")
x x5/4o5/2x3*b - ididdip
x o5/4x5/2x3*b - (contains "ike+3gad")
x x5/4x5/2x3*b - (contains "did+sidhei+gidhei")
(partial)
snubs and
holosnubs
...
...
...
  o o3/2o5/2o (µ=17) o o3/2o5/3o3*b (µ=18) o o5/3o5/3o5/2*b (µ=18)
quasiregular
components
x x3/2o5/2o - gipe
x o3/2x5/2o - giddip
x o3/2o5/2x - gissiddip
x x3/2o5/3o3*b - (contains "2ike")
x o3/2x5/3o3*b - sidtiddip
x o3/2o5/3x3*b - sidtiddip
x x5/3o5/3o5/2*b - (contains "2sissid")
x o5/3x5/3o5/2*b - (contains "2sissid")
other
Wythoffians
x x3/2x5/2o - (contains "2gike+sissid")
x x3/2o5/2x - qriddip
x o3/2x5/2x - (contains "2gad+ike")
x x3/2x5/2x - (contains "2gidtid+5cube")
x x3/2x5/3o3*b - (contains "sissid+3gike")
x x3/2o5/3x3*b - siidip
x o3/2x5/3x3*b - (contains "2geihid")
x x3/2x5/3x3*b - (contains "giddy+20{6/2}")
x x5/3x5/3o5/2*b - (contains "2gidhid")
x x5/3o5/3x5/2*b - (contains "2did")
x x5/3x5/3x5/2*b - (contains "2quitsissid")
(partial)
snubs and
holosnubs
...
...
...
  o o5/4o3o (µ=19) o o5/4o5/2o (µ=21) o o3/2o3/2o5/2*b (µ=22)
quasiregular
components
x x5/4o3o - dope
x o5/4x3o - iddip
x o5/4o3x - ipe
x x5/4o5/2o - gaddip
x o5/4x5/2o - diddip
x o5/4o5/2x - sissiddip
x x3/2o3/2o5/2*b - sidtiddip
x o3/2x3/2o5/2*b - (contains "2ike")
other
Wythoffians
x x5/4x3o - (contains "2sissid+gike")
x x5/4o3x - (contains gicdatrid)
x o5/4x3x - tipe
x x5/4x3x - (contains "ri+12{10/4}")
x x5/4x5/2o - (contains "3gissid")
x x5/4o5/2x - (contains cadditradid)
x o5/4x5/2x - (contains "3doe")
x x5/4x5/2x - (contains "2ditdid+5cube")
x x3/2x3/2o5/2*b - (contains "sissid+3gike")
x x3/2o3/2x5/2*b - (contains "2id")
x x3/2x3/2x5/2*b - (contains "4ike+2gad")
(partial)
snubs and
holosnubs
...
...
x s3/2s3/2s5/2*b - sirsiddip
...
  o o3/2o5/3o (µ=23) o o3/2o5/3o5/3*b (µ=26) o o5/4o5/3o (µ=27)
quasiregular
components
x x3/2o5/3o - gipe
x o3/2x5/3o - giddip
x o3/2o5/3x - gissiddip
x x3/2o5/3o5/3*b - (contains gacid)
x o3/2o5/3x5/3*b - (contains "2gissid")
x x5/4o5/3o - gaddip
x o5/4x5/3o - diddip
x o5/4o5/3x - sissiddip
other
Wythoffians
x x3/2x5/3o - (contains "2gike+sissid")
x x3/2o5/3x - (contains sicdatrid)
x o3/2x5/3x - quit gissiddip
x x3/2x5/3x - (contains "gird+20{6/2}")
x x3/2x5/3o5/3*b - (contains "2gid")
x x3/2o5/3x5/3*b - gaddiddip
x x3/2x5/3x5/3*b - (contains "2quitgissid")
x x5/4x5/3o - (contains "3gissid")
x x5/4o5/3x - radiddip
x o5/4x5/3x - quit sissiddip
x x5/4x5/3x - (contains "gird+12{10/4}")
(partial)
snubs and
holosnubs
x s3/2s5/3s - girsiddip
...
...
...
  o o5/4o3/2o (µ=29) o o5/4o3/2o5/3*b (µ=32) o o5/4o3/2o3/2*b (µ=34)
quasiregular
components
x x5/4o3/2o - dope
x o5/4x3/2o - iddip
x o5/4o3/2x - ipe
x x5/4o3/2o5/3*b - ditdiddip
x o5/4x3/2o5/3*b - (contains cid)
x o5/4o3/2x5/3*b - (contains gacid)
x x5/4o3/2o3/2*b - gidtiddip
x o5/4o3/2x3/2*b - (contains "2gike")
other
Wythoffians
x x5/4x3/2o - (contains "2sissid+gike")
x x5/4o3/2x - sriddip
x o5/4x3/2x - (contains "2ike+gad")
x x5/4x3/2x - (contains "2sidtid+5cube")
x x5/4x3/2o5/3*b - (contains "3sissid+gike")
x x5/4o3/2x5/3*b - (contains "sidtid+gidtid")
x o5/4x3/2x5/3*b - gidditdiddip
x x5/4x3/2x5/3*b - (contains "gid+geihid+gidhid")
x x5/4x3/2o3/2*b - (contains "2gid")
x x5/4o3/2x3/2*b - (contains "3ike+gad")
x x5/4x3/2x3/2*b - (contains 2sissid+4gike")
(partial)
snubs and
holosnubs
...
...
...
  o o5/4o5/4o3/2*b (µ=38) o o5/4o5/4o5/4*b (µ=42)  
quasiregular
components
x x5/4o5/4o3/2*b - (contains cid)
x o5/4x5/4o3/2*b - (contains "2doe")
x x5/4o5/4o5/4*b - (contains "2gad")
 
other
Wythoffians
x x5/4x5/4o3/2*b - (contains "sidtid+ditdid")
x x5/4o5/4x3/2*b - (contains "2id")
x x5/4x5/4x3/2*b - (contains "4sissid+2gike")
x x5/4x5/4o5/4*b - (contains "2did")
x x5/4x5/4x5/4*b - (contains "6gissid")
 
(partial)
snubs and
holosnubs
...
...
 


Duoprisms & Prismatic Prisms

  o-n/d-o o-m/b-o o o o-n/d-o o o o o
of
quasiregulars
x3o x3o         - triddip
x3o x4o         - tisdip
x4o x4o         - tes
...

x3o x-n-o       - 3,n-dip
x4o x-n-o       - 4,n-dip
...

x-n-o x-n-o     - n,n-dip
x-n-o x-m-o     - n,m-dip
x-n/d-o x-m/b-o - n/d,m/b-dip
x x x3o     - tisdip
x x x4o     - tes
...

x x x-n-o   - 4,n-dip
x x x-n/d-o - 4,n/d-dip
x x x x - tes
other
Wythoffians
x3x x3o     - thiddip
x3x x3x     - hiddip
x3o x4x     - todip
x3x x4o     - shiddip
x3x x4x     - hodip
x4o x4x     - sodip
...

x4o x-n-x   - 4,2n-dip
x4o x-n/d-x - 4,2n/d-dip
x3x x-n-o   - 6,n-dip
x4x x-n-o   - 8,n-dip
...

x-n-x x-m-o - 2n,m-dip
x-n-x x-m-x - 2n,2m-dip
x x x3x   - shiddip
x x x4x   - sodip
...

x x x-n-x - 4,2n-dip
 
(partial)
snubs and
holosnubs
s3s2x3o         - triddip
s3s x3o         - triddip
s3s2x3x         - thiddip
s3s x3x         - thiddip

s4o2s4o         - hex
s4x s4x         - tes
s4x2s4x         - (?) *)

s-n-s-2-s-m-s   - n,m-dap *)
s-2n-o-2-s-2m-o - n,m-dap *)
s-n-s-2-s-2m-x  - ... *)

s5/3s2s5s       - gudap

...
s2s2s4o        - hex
s2s2s3s        - 2,3-dap *)
...

x s2s4o        - tepe
x s-2-s-2n-o   - n-appip
x s-2-s-2n/d-o - n/d-appip

x s2s3s        - ope
x s2s4s        - squappip
...

x s-2-s-n-s    - n-appip
x s-2-s-n/d-s  - n/d-appip

x x s3s        - tisdip
...

x x s-n-s      - 4,n-dip

s-2-s-2-s-n-s  - 2,n-dap *)
s2s2s2s - hex

x s2s2s - tepe



other non-kaleidoscopical uniform polychora   (up)

acc. to other regiments making up own regiments
affic          (afdec regiment)   = hemi( x3x4x3x4*a4/3*c *b4/3*d )

chope          (cope regiment)

dard tipady    (dattady regiment)
dittadphi      (dattady regiment)
dittafady      (dattady regiment)   = hemi( x5o5/3x5o5/3*a3*c )
gidard tipady  (dattady regiment)
grad tathi     (dattady regiment)
gridtathi      (dattady regiment)
mardatathi     (dattady regiment)
ridatathi      (dattady regiment)

girdip         (gaddiddip regiment)   = reduced( x x3/2x5/3x , by x x3/2x )

gadathiphi     (gadtaxady regiment)   = reduced( x5/3o3x3/2o3*b , by 2tet )
gadtifady      (gadtaxady regiment)   = hemi( x5/2o3x5/2o3*a5/3*c )
gardatady      (gadtaxady regiment)   = reduced( x3/2o3o3o5/3*a5*c , by {5} )
gardatathi     (gadtaxady regiment)   = reduced( x5/3x5/3o3o5*a3/2*c , by gitphi )
gardtapaxhi    (gadtaxady regiment)

girpdo         (gichado regiment)

geihiddip      (giddip regiment)   = hemi( x o3/2x5/3x3*a )
gidhiddip      (giddip regiment)   = hemi( x x5/3x5/3o5/2*a )

gacdupthix     (gidipthi regiment)
gad phiddix    (gidipthi regiment)

gripady        (gippixady regiment)

girpdi         (gipti regiment)

gahfipto       (gittith regiment)
gaquipadah     (gittith regiment)
gittifcoth     (gittith regiment)
gnappoth       (gittith regiment)
picnut         (gittith regiment)

grohp          (goccope regiment)

gipriphi       (gwavixady regiment)   = reduced( x5/3x3o3/2x , by 2thah )

tho            (hex regiment)

dod honho      (ico regiment)
doh honho      (ico regiment)
ghahoh         (ico regiment)
hodho          (ico regiment)
hoh honho      (ico regiment)
hohoh          (ico regiment)
huhoh          (ico regiment)
ihi            (ico regiment)
odho           (ico regiment)
oh             (ico regiment)
ohuhoh         (ico regiment)
ratho          (ico regiment)
shahoh         (ico regiment)

thahp          (ope regiment)

sad phiddix    (padohi regiment)
scadupthix     (padohi regiment)

sripady        (prahi regiment)

ripdip         (prip regiment)

sirpdi         (prico regiment)

sirpdo         (prit regiment)

sirpaxhi       (prix regiment)

sirpith        (proh regiment)

girpixhi       (quippirgax regiment)

girpith        (quiproh regiment)

firgaghi       (ragaghi regiment)
mohiny         (ragaghi regiment)

prap vixhi     (ragishi regiment)
spapivady      (ragishi regiment)

firp           (rap regiment)   = hemi( x3o3o3/2x )
pinnip         (rap regiment)   = reduced( x3o3/2x3o , by 2thah )

fry            (rahi regiment)
shinhi         (rahi regiment)

firsashi       (rasishi regiment)
hinhi          (rasishi regiment)

frico          (rico regiment)
ini            (rico regiment)

frogfix        (rigfix regiment)
gipdohiny      (rigfix regiment)
gippapivady    (rigfix regiment)
graphi         (rigfix regiment)
mif pixady     (rigfix regiment)
ofpipixhi      (rigfix regiment)
omfapaxady     (rigfix regiment)
quiphi         (rigfix regiment)
ripahi         (rigfix regiment)   = reduced( x3o3/2x5/2o , by 2thah )

giprapivady    (righi regiment)
papvixhi       (righi regiment)

firgogishi     (rigogishi regiment)
gohiny         (rigogishi regiment)

dithix         (rissidtixhi regiment)
gaddit thix    (rissidtixhi regiment)
gidditdy       (rissidtixhi regiment)
gidditpix      (rissidtixhi regiment)
giddit thix    (rissidtixhi regiment)
gidthidy hi    (rissidtixhi regiment)
gotdatixhi     (rissidtixhi regiment)
gotditpix      (rissidtixhi regiment)
middit thix    (rissidtixhi regiment)
ridditdy       (rissidtixhi regiment)
sidditdy       (rissidtixhi regiment)
sidditpix      (rissidtixhi regiment)
siddit thix    (rissidtixhi regiment)
sidthidy hi    (rissidtixhi regiment)
stodatixhi     (rissidtixhi regiment)
stoditpix      (rissidtixhi regiment)
todithix       (rissidtixhi regiment)
todtixhi       (rissidtixhi regiment)

firt           (rit regiment)
gotto          (rit regiment)
hinnit         (rit regiment)
sto            (rit regiment)

frox           (rox regiment)   = reduced( x3o3/2x5o , by 2thah )
ipixady        (rox regiment)
lifpipixhi     (rox regiment)
nipixady       (rox regiment)
rixhi          (rox regiment)
sirphinady     (rox regiment)
sophi          (rox regiment)
sprapivady     (rox regiment)
sriphi         (rox regiment)

badohi         (sabbadipady regiment)
bithi          (sabbadipady regiment)
gabbadipady    (sabbadipady regiment)
gabbathi       (sabbadipady regiment)
gabippady      (sabbadipady regiment)
ganbathi       (sabbadipady regiment)
ganbippady     (sabbadipady regiment)
sabbathi       (sabbadipady regiment)
sabippady      (sabbadipady regiment)
sanbathi       (sabbadipady regiment)
sanbippady     (sabbadipady regiment)

dippit         (sidpith regiment)
iquipadah      (sidpith regiment)
shafipto       (sidpith regiment)
snappoth       (sidpith regiment)
stefacoth      (sidpith regiment)

six fipady     (sidpixhi regiment)

sadtifady      (sidtaxhi regiment)   = hemi( x5o3/2x5o3/2*a5*c )
sand tathi     (sidtaxhi regiment)   = reduced( x5x5o3o5/3*a3/2*c , by sitphi )
siddit paxhi   (sidtaxhi regiment)
sirdatady      (sidtaxhi regiment)   = reduced( x3/2o3o3o5*a5/3*c , by {5/2} )
sirdtapady     (sidtaxhi regiment)   = reduced( x5o3x3/2o3*b , by 2tet )

ditdidap       (sidtidap regiment)
gidtidap       (sidtidap regiment)

didhi          (sishi regiment)
getut          (sishi regiment)
gifdahihox     (sishi regiment)
gridaphi       (sishi regiment)
gridixhi       (sishi regiment)
idhi           (sishi regiment)
ofiddady       (sishi regiment)
paphacki       (sishi regiment)
paphicki       (sishi regiment)
setut          (sishi regiment)
sifdahihox     (sishi regiment)
sridaphi       (sishi regiment)
sridixhi       (sishi regiment)

inpac          (spic regiment)

nipdip         (spid regiment)
phud           (spid regiment)
piphid         (spid regiment)

pinpixhi       (srahi regiment)
spriphi        (srahi regiment)   = reduced( x5x3o3/2x , by 2thah )

garpop         (srip regiment)
pinnipdip      (srip regiment)
pippindip      (srip regiment)
pirpop         (srip regiment)   = reduced( x3x3o3/2x , by 2thah )
sirdop         (srip regiment)

pinpith        (srit regiment)
spript         (srit regiment)   = reduced( x4x3o3/2x , by 2thah )

titho          (thex regiment)

gapript        (wavitoth regiment)   = reduced( x4/3x3o3/2x , by 2thah )

...
gadsadox    (???) compound-member: [10raggix]

gap         (convex, edge skeleton is an ex sub-skeleton)

gidriddip

gisp        (edge skeleton is a gax sub-skeleton)

gondip      (edge skeleton is a gittith super-skeleton)

ondip       (edge skeleton is a sidpith super-skeleton)

padiap      (edge skeleton is a gax sub-skeleton)

rappisdi    (edge skeleton is a sishi sub-skeleton)

rapsady     (???)

sabbadipady (edge skeleton is join of quit sishi skeleton 
             with siddapady skeleton)

sadsadox    (???) compound-member: [10rox]

sidtidap    (heading the set of Johnson antiprisms)

sisp        (edge skeleton is an ex sub-skeleton)


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