Acronym	idasrid, id || srid, K-4.131
Name	icosidodecahedron atop small rhombicosidodecahedron, icosidodecahedron cupola, ike-first supra-cap of rox
Segmentochoron display
Circumradius	sqrt[5+2 sqrt(5)] = 3.077684
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	at {3} between oct and squippy:   arccos[-(1+3 sqrt(5))/8] = 164.477512° at {3} between oct and pap:   arccos(-sqrt[7+3 sqrt(5)]/4) = 157.761244° at {3} between pap and squippy:   arccos(-sqrt[7+3 sqrt(5)]/4) = 157.761244° at {5} between id and pap:   arccos[-(1+sqrt(5))/4] = 144° at {3} between id and oct:   arccos[-sqrt(5/8)] = 142.238756° at {4} between squippy and srid:   arccos[1/sqrt(2)] = 45° at {3} between oct and srid:   arccos[sqrt(5/8)] = 37.761244° at {5} between pap and srid:   arccos[(1+sqrt(5))/4] = 36°
Face vector	90, 300, 274, 64
Confer	uniform relative: rox   related segmentochora: antipentawedge   general polytopal classes: segmentochora   fundamental lace prisms
External links

It happens to be the second monostratic segment of rectified hexacosachoron in icosahedral direction.

Incidence matrix according to Dynkin symbol

ox3xo5ox&#x   → height = 1/2
(id || srid)

o.3o.5o.    | 30  * |  4   4  0  0 |  2  2  2  4  2  0  0  0 | 1  2  1  2 0
.o3.o5.o    |  * 60 |  0   2  2  2 |  0  0  2  1  2  1  2  1 | 0  1  2  1 1
------------+-------+--------------+-------------------------+-------------
.. x. ..    |  2  0 | 60   *  *  * |  1  1  0  1  0  0  0  0 | 1  1  0  1 0
oo3oo5oo&#x |  1  1 |  * 120  *  * |  0  0  1  1  1  0  0  0 | 0  1  1  1 0
.x .. ..    |  0  2 |  *   * 60  * |  0  0  1  0  0  1  1  0 | 0  1  1  0 1
.. .. .x    |  0  2 |  *   *  * 60 |  0  0  0  0  1  0  1  1 | 0  0  1  1 1
------------+-------+--------------+-------------------------+-------------
o.3x. ..    |  3  0 |  3   0  0  0 | 20  *  *  *  *  *  *  * | 1  1  0  0 0
.. x.5o.    |  5  0 |  5   0  0  0 |  * 12  *  *  *  *  *  * | 1  0  0  1 0
ox .. ..&#x |  1  2 |  0   2  1  0 |  *  * 60  *  *  *  *  * | 0  1  1  0 0
.. xo ..&#x |  2  1 |  1   2  0  0 |  *  *  * 60  *  *  *  * | 0  1  0  1 0
.. .. ox&#x |  1  2 |  0   2  0  1 |  *  *  *  * 60  *  *  * | 0  0  1  1 0
.x3.o ..    |  0  3 |  0   0  3  0 |  *  *  *  *  * 20  *  * | 0  1  0  0 1
.x .. .x    |  0  4 |  0   0  2  2 |  *  *  *  *  *  * 30  * | 0  0  1  0 1
.. .o5.x    |  0  5 |  0   0  0  5 |  *  *  *  *  *  *  * 12 | 0  0  0  1 1
------------+-------+--------------+-------------------------+-------------
o.3x.5o.    ♦ 30  0 | 60   0  0  0 | 20 12  0  0  0  0  0  0 | 1  *  *  * *
ox3xo ..&#x ♦  3  3 |  3   6  3  0 |  1  0  3  3  0  1  0  0 | * 20  *  * *
ox .. ox&#x ♦  1  4 |  0   4  2  2 |  0  0  2  0  2  0  1  0 | *  * 30  * *
.. xo5ox&#x ♦  5  5 |  5  10  0  5 |  0  1  0  5  5  0  0  1 | *  *  * 12 *
.x3.o5.x    ♦  0 60 |  0   0 60 60 |  0  0  0  0  0 20 30 12 | *  *  *  * 1