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+3 sqrt(5)]/4) = 157.761244°
  • at {3} between oct and peppy:   arccos(-sqrt[7+3 sqrt(5)]/4) = 157.761244°
  • at {5} between id and peppy:   36°
  • at {3} between id and oct:   arccos(sqrt[7+3 sqrt(5)]/4) = 22.238756°
Face vector 42, 150, 142, 34
Confer
uniform relative:
rox  
related CRFs:
line || bilbiro   {3} || thawro   rite  
related segmentochora:
gyepipa pero   papaid   peppia pero   teddi aid  
ambification pre-image:
ikepy  
general polytopal classes:
segmentochora   fundamental lace prisms  
External
links 		polytopewiki  

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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