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

The analysis of the being used lacing facets shows that the half-height section results in a half-edge sized qrid.

Incidence matrix according to Dynkin symbol

xo3oo5/3ox&#x   → height = 1/2
(narrower gike || gissid)

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