Acronym ..., ike || id, K-4.137
Name icosahedron atop icosidodecahedron,
icosahedral cap of rectified hexacosachoron,
icosahedral cupola
Segmentochoron display
Circumradius sqrt[5+2 sqrt(5)] = 3.077684
Lace city
in approx. ASCII-art
    x5o
       
       
o5o    
    o5f
       
       
x5o    
       
       
    x5x
       
       
o5x    
       
       
    f5o
o5o    
       
       
    o5x
        x3o   o3f f3o   o3x        
                                   		F=ff=x+f=2x+v
o3x   x3f F3o   f3f   o3F f3x   x3o
Dihedral angles
  • at {3} between oct and oct:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between ike and oct:   arccos(-sqrt[7+3sqrt(5)]/4) = 157.761244°
  • at {3} between oct and peppy:   arccos(-sqrt[7+3sqrt(5)]/4) = 157.761244°
  • at {5} between id and peppy:   36°
  • at {3} between id and oct:   arccos(sqrt[7+3sqrt(5)]/4) = 22.238756°
Confer
uniform relative:
rox  
related CRFs:
line || bilbiro   {3} || thawro  

Incidence matrix according to Dynkin symbol

xo3ox5oo&#x   → height = (sqrt(5)-1)/4 = 0.309017
(ike || id)

o.3o.5o.    | 12  *   5  5  0 |  5  5  5  0  0 | 1  5  1 0
.o3.o5.o    |  * 30 |  0  2  4 |  0  1  4  2  2 | 0  2  2 1
------------+-------+----------+----------------+----------
x. .. ..    |  2  0 | 30  *  * |  2  1  0  0  0 | 1  2  0 0
oo3oo5oo&#x |  1  1 |  * 60  * |  0  1  2  0  0 | 0  2  1 0
.. .x ..    |  0  2 |  *  * 60 |  0  0  1  1  1 | 0  1  1 1
------------+-------+----------+----------------+----------
x.3o. ..    |  3  0 |  3  0  0 | 20  *  *  *  * | 1  1  0 0
xo .. ..&#x |  2  1 |  1  2  0 |  * 30  *  *  * | 0  2  0 0
.. ox ..&#x |  1  2 |  0  2  1 |  *  * 60  *  * | 0  1  1 0
.o3.x ..    |  0  3 |  0  0  3 |  *  *  * 20  * | 0  1  0 1
.. .x5.o    |  0  5 |  0  0  5 |  *  *  *  * 12 | 0  0  1 1
------------+-------+----------+----------------+----------
x.3o.5o.     12  0 | 30  0  0 | 20  0  0  0  0 | 1  *  * *
xo3ox ..&#x   3  3 |  3  6  3 |  1  3  3  1  0 | * 20  * *
.. ox5oo&#x   1  5 |  0  5  5 |  0  0  5  0  1 | *  * 12 *
.o3.x5.o      0 30 |  0  0 60 |  0  0  0 20 12 | *  *  * 1

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