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As abstract polytope gikaike is automorph, therby interchanging ike with gike.

Its vertex figures above are displayed to be edge-faceting of sidtid and therfore mere facetings of a v-scaled doe. Therfrom it becomes evident that this polychoron itself occurs as an edge-faceting within sishi.

It was found by Mecejide in early 2023. It further is notable because all its facets are regular polyhedra. And because all its faces moreover are triangles only, it even allows for rectification and truncation, then resulting in regikaike and tigikaike respectively.

In summer 2024 then found "puffer fish" 2 edge-facetings therof: one additionally using the circumscribing pentagrams of gike (sirgikaike) and one additionally using the inscribing pentagons of ike (girgikaike). Both also replace the lacing octs between nearby triangles each by lacing trips towards the respective triangle at the far side each. This is where the -r- (retro) in their names originates from.

Incidence matrix

gike || ike   → height = 1/2

12  * |  5  5  0 |  5 10  5  0 | 1  5  5 0 verf = stiscu
 * 12 |  0  5  5 |  0  5 10  5 | 0  5  5 1 verf = rapescu
------+----------+-------------+----------
 2  0 | 30  *  * |  2  2  0  0 | 1  2  1 0
 1  1 |  * 60  * |  0  2  2  0 | 0  2  2 0
 0  2 |  *  * 30 |  0  0  2  2 | 0  2  1 1
------+----------+-------------+----------
 3  0 |  3  0  0 | 20  *  *  * | 1  1  0 0
 2  1 |  1  2  0 |  * 60  *  * | 0  1  1 0
 1  2 |  0  2  1 |  *  * 60  * | 0  1  1 0
 0  3 |  0  0  3 |  *  *  * 20 | 0  1  0 1
------+----------+-------------+----------
12  0 | 30  0  0 | 20  0  0  0 | 1  *  * * gike
 3  3 |  3  6  3 |  1  3  3  1 | * 20  * * oct
 2  2 |  1  4  1 |  0  2  2  0 | *  * 30 * tet
 0 12 |  0  0 30 |  0  0  0 20 | *  *  * 1 ike