Acronym gikagid, gike || gid
Name great icosahedron atop great icosidodecahedron,
great icosahedral cap of rectified grand hexacosachoron,
great-icosahedral cupola
Circumradius sqrt[5-2 sqrt(5)] = 0.726543
Confer
uniform relative:
raggix  
general polytopal classes:
segmentochora  

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

Incidence matrix according to Dynkin symbol

xo3ox5/2oo&#x   → height = (1+sqrt(5))/4 = 0.809017
(gike || gid)

o.3o.5/2o.    | 12  *   5  5  0 |  5  5  5  0  0 | 1  5  1 0
.o3.o5/2.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
oo3oo5/2oo&#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
.. .x5/2.o    |  0  5 |  0  0  5 |  *  *  *  * 12 | 0  0  1 1
--------------+-------+----------+----------------+----------
x.3o.5/2o.     12  0 | 30  0  0 | 20  0  0  0  0 | 1  *  * *
xo3ox   ..&#x   3  3 |  3  6  3 |  1  3  3  1  0 | * 20  * *
.. ox5/2oo&#x   1  5 |  0  5  5 |  0  0  5  0  1 | *  * 12 *
.o3.x5/2.o      0 30 |  0  0 60 |  0  0  0 20 12 | *  *  * 1

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