Acronym ...
Name mono-diminished vertex-first rotunda of hexacosachoron
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art 
            o5o       
                   o5x
                      
       x5o            
o5o                   
                   f5o
            o5f       
                      
o5x                   
       f5o            
                      
                   x5x
                      
       o5f            
x5o                   
                      
            f5o       
                   o5f
o5o                   
       o5x            
                      
                   x5o
            o5o       

        x3o   o3f f3o   o3x        
                                   
                                       (F=ff)
 o3o o3f   f3x       x3f   f3o o3o 
                                   
   f3o       o3F   F3o       o3f   
                                   
                                   
o3x   x3f F3o   f3f   o3F f3x   x3o
Dihedral angles
  • at {3} between tet and tet:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between ike and tet:   arccos[-sqrt(5/8)] = 142.238756°
  • at {3} between peppy and tet:   arccos[-sqrt(5/8)] = 142.238756°
  • at {5} between id and peppy:   108°
  • at {3} between tet and id:   arccos[(3-sqrt(5))/sqrt(32)] = 82.238756°
Face vector 74, 372, 562, 264
Confer
segmentochora:
ikepy   ike || doe   doe || id  
other CRFs:
rotunda of ex   pt || ike || doe || id   ike || doe || id   ike || f-ike || id  
uniform relative:
ex  

Incidence matrix according to Dynkin symbol

xofo3ooox5oxoo&#xt   → height(1,2) = height(3,4) = 1/2
                                      height(2,3) = (sqrt(5)-1)/4 = 0.309017
(ike || pseudo doe || pseudo f-ike || id)

o...3o...5o...     | 12  *  *  * ♦  5  5  1  0  0  0  0  0 |  5 10  5  5  0  0  0   0  0  0  0 | 1  5  5  5  0  0  0  0 0
.o..3.o..5.o..     |  * 20  *  * ♦  0  3  0  3  3  3  0  0 |  0  3  6  3  6  3  3   6  0  0  0 | 0  1  3  6  1  3  6  0 0
..o.3..o.5..o.     |  *  * 12  * ♦  0  0  1  0  5  0  5  0 |  0  0  0  5  5  0  0  10  5  0  0 | 0  0  0  5  0  5  5  1 0
...o3...o5...o     |  *  *  * 30 |  0  0  0  0  0  2  2  4 |  0  0  0  0  0  4  1   4  4  2  2 | 0  0  0  0  2  4  2  2 1
-------------------+-------------+-------------------------+-----------------------------------+-------------------------
x... .... ....     |  2  0  0  0 | 30  *  *  *  *  *  *  * |  2  2  0  0  0  0  0   0  0  0  0 | 1  2  1  0  0  0  0  0 0
oo..3oo..5oo..&#x  |  1  1  0  0 |  * 60  *  *  *  *  *  * |  0  2  2  1  0  0  0   0  0  0  0 | 0  1  2  2  0  0  0  0 0
o.o.3o.o.5o.o.&#x  |  1  0  1  0 |  *  * 12  *  *  *  *  * |  0  0  0  5  0  0  0   0  0  0  0 | 0  0  0  5  0  0  0  0 0
.... .... .x..     |  0  2  0  0 |  *  *  * 30  *  *  *  * |  0  0  2  0  2  0  1   0  0  0  0 | 0  0  1  2  0  0  2  0 0
.oo.3.oo.5.oo.&#x  |  0  1  1  0 |  *  *  *  * 60  *  *  * |  0  0  0  1  2  0  0   2  0  0  0 | 0  0  0  2  0  1  2  0 0
.o.o3.o.o5.o.o&#x  |  0  1  0  1 |  *  *  *  *  * 60  *  * |  0  0  0  0  0  2  1   2  0  0  0 | 0  0  0  0  1  2  2  0 0
..oo3..oo5..oo&#x  |  0  0  1  1 |  *  *  *  *  *  * 60  * |  0  0  0  0  0  0  0   2  2  0  0 | 0  0  0  0  0  2  1  1 0
.... ...x ....     |  0  0  0  2 |  *  *  *  *  *  *  * 60 |  0  0  0  0  0  1  0   0  1  1  1 | 0  0  0  0  1  1  0  1 1
-------------------+-------------+-------------------------+-----------------------------------+-------------------------
x...3o... ....     |  3  0  0  0 |  3  0  0  0  0  0  0  0 | 20  *  *  *  *  *  *   *  *  *  * | 1  1  0  0  0  0  0  0 0
xo.. .... ....&#x  |  2  1  0  0 |  1  2  0  0  0  0  0  0 |  * 60  *  *  *  *  *   *  *  *  * | 0  1  1  0  0  0  0  0 0
.... .... ox..&#x  |  1  2  0  0 |  0  2  0  1  0  0  0  0 |  *  * 60  *  *  *  *   *  *  *  * | 0  0  1  1  0  0  0  0 0
ooo.3ooo.5ooo.&#x  |  1  1  1  0 |  0  1  1  0  1  0  0  0 |  *  *  * 60  *  *  *   *  *  *  * | 0  0  0  2  0  0  0  0 0
.... .... .xo.&#x  |  0  2  1  0 |  0  0  0  1  2  0  0  0 |  *  *  *  * 60  *  *   *  *  *  * | 0  0  0  1  0  0  1  0 0
.... .o.x ....&#x  |  0  1  0  2 |  0  0  0  0  0  2  0  1 |  *  *  *  *  * 60  *   *  *  *  * | 0  0  0  0  1  1  0  0 0
.... .... .x.o&#x  |  0  2  0  1 |  0  0  0  1  0  2  0  0 |  *  *  *  *  *  * 30   *  *  *  * | 0  0  0  0  0  0  2  0 0
.ooo3.ooo5.ooo&#x  |  0  1  1  1 |  0  0  0  0  1  1  1  0 |  *  *  *  *  *  *  * 120  *  *  * | 0  0  0  0  0  1  1  0 0
.... ..ox ....&#x  |  0  0  1  2 |  0  0  0  0  0  0  2  1 |  *  *  *  *  *  *  *   * 60  *  * | 0  0  0  0  0  1  0  1 0
...o3...x ....     |  0  0  0  3 |  0  0  0  0  0  0  0  3 |  *  *  *  *  *  *  *   *  * 20  * | 0  0  0  0  1  0  0  0 1
.... ...x5...o     |  0  0  0  5 |  0  0  0  0  0  0  0  5 |  *  *  *  *  *  *  *   *  *  * 12 | 0  0  0  0  0  0  0  1 1
-------------------+-------------+-------------------------+-----------------------------------+-------------------------
x...3o...5o...     ♦ 12  0  0  0 | 30  0  0  0  0  0  0  0 | 20  0  0  0  0  0  0   0  0  0  0 | 1  *  *  *  *  *  *  * *
xo..3oo.. ....&#x  ♦  3  1  0  0 |  3  3  0  0  0  0  0  0 |  1  3  0  0  0  0  0   0  0  0  0 | * 20  *  *  *  *  *  * *
xo.. .... ox..&#x  ♦  2  2  0  0 |  1  4  0  1  0  0  0  0 |  0  2  2  0  0  0  0   0  0  0  0 | *  * 30  *  *  *  *  * *
.... .... oxo.&#xt ♦  1  2  1  0 |  0  2  1  1  2  0  0  0 |  0  0  1  2  1  0  0   0  0  0  0 | *  *  * 60  *  *  *  * *
.o.o3.o.x ....&#x  ♦  0  1  0  3 |  0  0  0  0  0  3  0  3 |  0  0  0  0  0  3  0   0  0  1  0 | *  *  *  * 20  *  *  * *
.... .oox ....&#xt ♦  0  1  1  2 |  0  0  0  0  1  2  2  1 |  0  0  0  0  0  1  0   2  1  0  0 | *  *  *  *  * 60  *  * *
.... .... .xoo&#xt ♦  0  2  1  1 |  0  0  0  1  2  2  1  0 |  0  0  0  0  1  0  1   2  0  0  0 | *  *  *  *  *  * 60  * *
.... ..ox5..oo&#x  ♦  0  0  1  5 |  0  0  0  0  0  0  5  5 |  0  0  0  0  0  0  0   0  5  0  1 | *  *  *  *  *  *  * 12 *
...o3...x5...o     ♦  0  0  0 30 |  0  0  0  0  0  0  0 60 |  0  0  0  0  0  0  0   0  0 20 12 | *  *  *  *  *  *  *  * 1

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