Acronym ikaid, 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  

As abstract polytope ikaid is isomorphe to gikagid, thereby replacing pentagons by pentagrams, resp. ike by gike, peppy by stappy, and id by gid.

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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