As abstract polytope regikaike is automorph, therby interchanging pentagrams with pentagons, resp. gid with id and stiscu with rapescu.

It is quite remarkable that gikaike allows for some of the same operations as regulars do: this polychoron is nothing but the rectification operation being applied to it.

It happens, that it is an edge-faceting of rissidtixhi. (Note that sidtixhi itself is a sishi regiment member, which in turn had been the regimement of gikaike.)

Incidence matrix

gid || pseudo ri || id   → both heights = 1/2

30  *  * |  4   4  0  0   0  0 |  2  2  4  2  2  0  0  0  0  0 | 1  2  2  1  0 0
 * 60  * |  0   2  2  2   2  0 |  0  0  2  2  2  2  2  2  0  0 | 0  1  2  2  1 0
 *  * 30 |  0   0  0  0   4  4 |  0  0  0  0  0  4  2  2  2  2 | 0  0  2  1  2 1
---------+---------------------+-------------------------------+----------------
 2  0  0 | 60   *  *  *   *  * |  1  1  1  0  0  0  0  0  0  0 | 1  1  1  0  0 0
 1  1  0 |  * 120  *  *   *  * |  0  0  1  1  1  0  0  0  0  0 | 0  1  1  1  0 0
 0  2  0 |  *   * 60  *   *  * |  0  0  0  1  0  1  0  1  0  0 | 0  0  1  1  1 0
 0  2  0 |  *   *  * 60   *  * |  0  0  1  0  1  0  1  0  0  0 | 0  1  1  1  0 0
 0  1  1 |  *   *  *  * 120  * |  0  0  0  0  0  1  1  1  0  0 | 0  0  1  1  1 0
 0  0  2 |  *   *  *  *   * 60 |  0  0  0  0  0  1  0  0  1  1 | 0  0  1  0  1 1
---------+---------------------+-------------------------------+----------------
 3  0  0 |  3   0  0  0   0  0 | 20  *  *  *  *  *  *  *  *  * | 1  0  1  0  0 0
 5  0  0 |  5   0  0  0   0  0 |  * 12  *  *  *  *  *  *  *  * | 1  1  0  0  0 0  {5/2}
 2  2  0 |  1   2  0  1   0  0 |  *  * 60  *  *  *  *  *  *  * | 0  1  1  0  0 0
 1  2  0 |  0   2  1  0   0  0 |  *  *  * 60  *  *  *  *  *  * | 0  0  1  1  0 0
 1  2  0 |  0   2  0  1   0  0 |  *  *  *  * 60  *  *  *  *  * | 0  1  0  1  0 0
 0  2  2 |  0   0  1  0   2  1 |  *  *  *  *  * 60  *  *  *  * | 0  0  1  0  1 0
 0  2  1 |  0   0  0  1   2  0 |  *  *  *  *  *  * 60  *  *  * | 0  0  1  1  0 0
 0  2  1 |  0   0  1  0   2  0 |  *  *  *  *  *  *  * 60  *  * | 0  0  0  1  1 0
 0  0  3 |  0   0  0  0   0  3 |  *  *  *  *  *  *  *  * 20  * | 0  0  1  0  0 1
 0  0  5 |  0   0  0  0   0  5 |  *  *  *  *  *  *  *  *  * 12 | 0  0  0  0  1 1  {5}
---------+---------------------+-------------------------------+----------------
30  0  0 | 60   0  0  0   0  0 | 20 12  0  0  0  0  0  0  0  0 | 1  *  *  *  * *  gid
 5  5  0 |  5  10  0  5   0  0 |  0  1  5  0  5  0  0  0  0  0 | * 12  *  *  * *  stiscu
 3  6  3 |  3   6  3  3   6  3 |  1  0  3  3  0  3  3  0  1  0 | *  * 20  *  * *  co
 1  4  1 |  0   4  2  2   4  0 |  0  0  0  2  2  0  2  2  0  0 | *  *  * 30  * *  oct
 0  5  5 |  0   0  5  0  10  5 |  0  0  0  0  0  5  0  5  0  1 | *  *  *  * 12 *  rapescu
 0  0 30 |  0   0  0  0   0 60 |  0  0  0  0  0  0  0  0 20 12 | *  *  *  *  * 1  id