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

Incidence matrix according to Dynkin symbol

ox5oo5/2oo3oo&#x   → height = 0
(pt || gaghi)

o.5o.5/2o.3o.    | 1   * ♦ 120    0 | 1200   0 | 720   0 | 120 0
.o5.o5/2.o3.o    | * 120 |   1   20 |   20  30 |  30  12 |  12 1
-----------------+-------+----------+----------+---------+------
oo5oo5/2oo3oo&#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.o   .. ..    | 0   5 |   0    5 |    * 720 |   1   2 |   2 1
-----------------+-------+----------+----------+---------+------
ox5oo   .. ..&#x ♦ 1   5 |   5    5 |    5   1 | 720   * |   2 0
.x5.o5/2.o ..    ♦ 0  12 |   0   30 |    0  12 |   * 120 |   1 1
-----------------+-------+----------+----------+---------+------
ox5oo5/2oo ..&#x ♦ 1  12 |  12   30 |   30  12 |  12   1 | 120 *
.x5.o5/2.o3.o    ♦ 0 120 |   0 1200 |    0 720 |   0 120 |   * 1