As abstract polytope gissid || gike occurs itself in 2 isomorphic variants with exactly the same incidences: the taller one here, the antiprism, where the first type vertex figure in turn is a pentagonal antiprism variant, and the narrower one, the gissid-gike retroprism, where that vertex figure acts as a pentagonal retroprism variant instead.

Furthermore those are isomorphic to ikadoe, thereby replacing pentagrams by pentagons resp. replacing gissids by does, gikes by ikes, and stappies by peppies. In fact that one then will be the conjugate to the retroprism.

Incidence matrix according to Dynkin symbol

xo3oo5/2ox&#x   → height = sqrt[4 sqrt(5)-7]/2 = 0.697186
(taller gike || gissid)

o.3o.5/2o.    | 12  * |  5  5  0 |  5 10  5  0 | 1  5  5  1 0
.o3.o5/2.o    |  * 20 |  0  3  3 |  0  3  6  3 | 0  1  3  3 1
--------------+-------+----------+-------------+-------------
x. ..   ..    |  2  0 | 30  *  * |  2  2  0  0 | 1  2  1  0 0
oo3oo5/2oo&#x |  1  1 |  * 60  * |  0  2  2  0 | 0  1  2  1 0
.. ..   .x    |  0  2 |  *  * 30 |  0  0  2  2 | 0  0  1  2 1
--------------+-------+----------+-------------+-------------
x.3o.   ..    |  3  0 |  3  0  0 | 20  *  *  * | 1  1  0  0 0
xo ..   ..&#x |  2  1 |  1  2  0 |  * 60  *  * | 0  1  1  0 0
.. ..   ox&#x |  1  2 |  0  2  1 |  *  * 60  * | 0  0  1  1 0
.. .o5/2.x    |  0  5 |  0  0  5 |  *  *  * 12 | 0  0  0  1 1
--------------+-------+----------+-------------+-------------
x.3o.5/2o.    ♦ 12  0 | 30  0  0 | 20  0  0  0 | 1  *  *  * *
xo3oo   ..&#x ♦  3  1 |  3  3  0 |  1  3  0  0 | * 20  *  * *
xo ..   ox&#x ♦  2  2 |  1  4  1 |  0  2  2  0 | *  * 30  * *
.. oo5/2ox&#x ♦  1  5 |  0  5  5 |  0  0  5  1 | *  *  * 12 *
.o3.o5/2.x    ♦  0 20 |  0  0 30 |  0  0  0 12 | *  *  *  * 1