It either can be thought of as a degenerate 5D segmentotope with zero height, or as a 4D euclidean decomposition of the larger base into smaller bits.

As abstract polytope sishipy is isomorphic to gaghipy, thereby replacing pentagrams by pentagons, resp. sissid by gad and stappy by peppy, resp. sissidpy by gadpy and sishi by gaghi.

Incidence matrix according to Dynkin symbol

ox5/2oo5oo3oo&#x   → height = 0
(pt || sishi)

o.5/2o.5o.3o.    | 1   * ♦ 120    0 | 1200   0 | 720   0 | 120 0
.o5/2.o5.o3.o    | * 120 |   1   20 |   20  30 |  30  12 |  12 1
-----------------+-------+----------+----------+---------+------
oo5/2oo5oo3oo&#x | 1   1 | 120    * ♦   20   0 |  30   0 |  12 0
.x   .. .. ..    | 0   2 |   * 1200 |    1   3 |   3   3 |   3 1
-----------------+-------+----------+----------+---------+------
ox   .. .. ..&#x | 1   2 |   2    1 | 1200   * |   3   0 |   3 0
.x5/2.o .. ..    | 0   5 |   0    5 |    * 720 |   1   2 |   2 1
-----------------+-------+----------+----------+---------+------
ox5/2oo .. ..&#x ♦ 1   5 |   5    5 |    5   1 | 720   * |   2 0
.x5/2.o5.o ..    ♦ 0  12 |   0   30 |    0  12 |   * 120 |   1 1
-----------------+-------+----------+----------+---------+------
ox5/2oo5oo ..&#x ♦ 1  12 |  12   30 |   30  12 |  12   1 | 120 *
.x5/2.o5.o3.o    ♦ 0 120 |   0 1200 |    0 720 |   0 120 |   * 1