Acronym ...
Name pentadiminished 2/10-luna of hexacosachoron
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art
            o5o       
                   o5x
                      
                      
o5o                   
                   f5o
            o5f       
                      
o5x                   
       f5o            
                      
                   x5x
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {3} between tet and tet:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between mibdi and tet:   arccos[-sqrt(5/8)] = 142.238756°
  • at {3} between peppy and tet:   arccos[-sqrt(5/8)] = 142.238756°
  • at {3} between mibdi and peppy:   arccos[-(3 sqrt(5)-1)/8] = 135.522488°
  • at {3} between mibdi and pero:   arccos[-(3 sqrt(5)-1)/8] = 135.522488°
  • at {3} between peppy and peppy:   arccos[-(3 sqrt(5)-1)/8] = 135.522488°
  • at {5} between peppy and pero:   108°
  • at {3} between tet and pero:   arccos[(3-sqrt(5))/sqrt(32)] = 82.238756°
  • at {5} between mibdi and mibdi:   72°
  • at {10} between pero and pero:   72°
Confer
uniform relative:
ex  
related CRFs:
2/10-luna of ex   3 mibdies laced wedge  

The special edge with 5 incident mibdies of this polychoron (each being adjoined with their special wedge edge) also allows for a 3-fold counterpart: xfox2oxfo3ooox&#xt. (A 4-fold version does not exist, so.)

This polychoron happens to be just a diminishing of 2/10-luna of ex. In fact, the latter one is re-obtained when augmenting the mibdies by according pyramids.


Incidence matrix according to Dynkin symbol

xfoxo2oxfox5ooofx&#xt   → height(1,2) = sqrt[(5+sqrt(5))/40] = 0.425325
                          height(2,3) = sqrt[(5-sqrt(5))/40] = 0.262866
                          height(3,4) = sqrt[(5-2 sqrt(5))/20] = 0.162460
                          height(4,5) = sqrt[(5+2 sqrt(5))/20] = 0.688191

o....2o....5o....     | 2  * *  *  * | 1  5  0  0  0  0  0 0  0 0 0 | 5  5 0  0  0  0  0  0 0  0  0 0 | 5 1 0  0  0 0
.o...2.o...5.o...     | * 10 *  *  * | 0  1  2  1  2  0  0 0  0 0 0 | 1  2 1  2  1  2  0  0 0  0  0 0 | 2 1 1  1  0 0
..o..2..o..5..o..     | *  * 5  *  * | 0  0  0  2  0  4  2 0  0 0 0 | 1  0 0  0  0  4  2  4 1  0  0 0 | 2 0 0  2  2 0
...o.2...o.5...o.     | *  * * 10  * | 0  0  0  0  2  2  0 1  2 0 0 | 0  0 0  1  2  2  2  2 0  2  1 0 | 1 0 1  2  2 1
....o2....o5....o     | *  * *  * 10 | 0  0  0  0  0  0  1 0  2 1 1 | 0  0 0  0  2  0  0  2 1  1  2 1 | 0 0 2  2  1 1
----------------------+--------------+------------------------------+---------------------------------+--------------
x.... ..... .....     | 2  0 0  0  0 | 1  *  *  *  *  *  * *  * * * | 5  0 0  0  0  0  0  0 0  0  0 0 | 5 0 0  0  0 0
oo...2oo...5oo...&#x  | 1  1 0  0  0 | * 10  *  *  *  *  * *  * * * | 1  2 0  0  0  0  0  0 0  0  0 0 | 2 1 0  0  0 0
..... .x... .....     | 0  2 0  0  0 | *  * 10  *  *  *  * *  * * * | 0  1 1  1  0  0  0  0 0  0  0 0 | 1 1 1  0  0 0
.oo..2.oo..5.oo..&#x  | 0  1 1  0  0 | *  *  * 10  *  *  * *  * * * | 1  0 0  0  0  2  0  0 0  0  0 0 | 2 0 0  1  0 0
.o.o.2.o.o.5.o.o.&#x  | 0  1 0  1  0 | *  *  *  * 20  *  * *  * * * | 0  0 0  1  1  1  0  0 0  0  0 0 | 1 0 1  1  0 0
..oo.2..oo.5..oo.&#x  | 0  0 1  1  0 | *  *  *  *  * 20  * *  * * * | 0  0 0  0  0  1  1  1 0  0  0 0 | 1 0 0  1  1 0
..o.o2..o.o5..o.o&#x  | 0  0 1  0  1 | *  *  *  *  *  * 10 *  * * * | 0  0 0  0  0  0  0  2 1  0  0 0 | 0 0 0  2  1 0
...x. ..... .....     | 0  0 0  2  0 | *  *  *  *  *  *  * 5  * * * | 0  0 0  0  0  0  2  0 0  2  0 0 | 1 0 0  0  2 1
...oo2...oo5...oo&#x  | 0  0 0  1  1 | *  *  *  *  *  *  * * 20 * * | 0  0 0  0  1  0  0  1 0  1  1 0 | 0 0 1  1  1 1
..... ....x .....     | 0  0 0  0  2 | *  *  *  *  *  *  * *  * 5 * | 0  0 0  0  0  0  0  0 0  0  2 1 | 0 0 2  0  0 1
..... ..... ....x     | 0  0 0  0  2 | *  *  *  *  *  *  * *  * * 5 | 0  0 0  0  2  0  0  0 1  0  0 1 | 0 0 2  2  0 0
----------------------+--------------+------------------------------+---------------------------------+--------------
xfo.. ..... .....&#xt | 2  2 1  0  0 | 1  2  0  2  0  0  0 0  0 0 0 | 5  * *  *  *  *  *  * *  *  * * | 2 0 0  0  0 0
..... ox... .....&#x  | 1  2 0  0  0 | 0  2  1  0  0  0  0 0  0 0 0 | * 10 *  *  *  *  *  * *  *  * * | 1 1 0  0  0 0
..... .x...5.o...     | 0  5 0  0  0 | 0  0  5  0  0  0  0 0  0 0 0 | *  * 2  *  *  *  *  * *  *  * * | 0 1 1  0  0 0
..... .x.o. .....&#x  | 0  2 0  1  0 | 0  0  1  0  2  0  0 0  0 0 0 | *  * * 10  *  *  *  * *  *  * * | 1 0 1  0  0 0
..... ..... .o.fx&#xt | 0  1 0  2  2 | 0  0  0  0  2  0  0 0  2 0 1 | *  * *  * 10  *  *  * *  *  * * | 0 0 1  1  0 0
.ooo.2.ooo.5.ooo.&#x  | 0  1 1  1  0 | 0  0  0  1  1  1  0 0  0 0 0 | *  * *  *  * 20  *  * *  *  * * | 1 0 0  1  0 0
..ox. ..... .....&#x  | 0  0 1  2  0 | 0  0  0  0  0  2  0 1  0 0 0 | *  * *  *  *  * 10  * *  *  * * | 1 0 0  0  1 0
..ooo2..ooo5..ooo&#x  | 0  0 1  1  1 | 0  0  0  0  0  1  1 0  1 0 0 | *  * *  *  *  *  * 20 *  *  * * | 0 0 0  1  1 0
..... ..... ..o.x&#x  | 0  0 1  0  2 | 0  0  0  0  0  0  2 0  0 0 1 | *  * *  *  *  *  *  * 5  *  * * | 0 0 0  2  0 0
...xo ..... .....&#x  | 0  0 0  2  1 | 0  0  0  0  0  0  0 1  2 0 0 | *  * *  *  *  *  *  * * 10  * * | 0 0 0  0  1 1
..... ...ox .....&#x  | 0  0 0  1  2 | 0  0  0  0  0  0  0 0  2 1 0 | *  * *  *  *  *  *  * *  * 10 * | 0 0 1  0  0 1
..... ....x5....x     | 0  0 0  0 10 | 0  0  0  0  0  0  0 0  0 5 5 | *  * *  *  *  *  *  * *  *  * 1 | 0 0 2  0  0 0
----------------------+--------------+------------------------------+---------------------------------+--------------
xfox.2oxfo. .....&#xt  2  4 2  2  0 | 1  4  2  4  4  4  0 1  0 0 0 | 2  2 0  2  0  4  2  0 0  0  0 0 | 5 * *  *  * *
..... ox...5oo...&#x   1  5 0  0  0 | 0  5  5  0  0  0  0 0  0 0 0 | 0  5 1  0  0  0  0  0 0  0  0 0 | * 2 *  *  * *
..... .x.ox5.o.fx&#xt  0  5 0  5 10 | 0  0  5  0 10  0  0 0 10 5 5 | 0  0 1  5  5  0  0  0 0  0  5 1 | * * 2  *  * *
..... ..... .oofx&#xr  0  1 1  2  2 | 0  0  0  1  2  2  2 0  2 0 1 | 0  0 0  0  1  2  0  2 1  0  0 0 | * * * 10  * * cycle: (BCFE)
..oxo ..... .....&#x   0  0 1  2  1 | 0  0  0  0  0  2  1 1  2 0 0 | 0  0 0  0  0  0  1  2 0  1  0 0 | * * *  * 10 *
...xo2...ox .....&#x   0  0 0  2  2 | 0  0  0  0  0  0  0 1  4 1 0 | 0  0 0  0  0  0  0  0 0  2  2 0 | * * *  *  * 5

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