As abstract polytope gissidagid is isomorphic to doaid, thereby replacing pentagrams by pentagons resp. replacing gissids by does, staps by paps, and gids by ids.

Incidence matrix according to Dynkin symbol

oo3ox5/2xo&#x   → height = sqrt[(15 sqrt(5)-29)/8] = 0.753411
(gissid || gid)

o.3o.5/2o.    | 20  * |  3  3  0 |  3  3  3  0  0 | 1  1  3 0
.o3.o5/2.o    |  * 30 |  0  2  4 |  0  4  1  2  2 | 0  2  2 1
--------------+-------+----------+----------------+----------
.. ..   x.    |  2  0 | 30  *  * |  2  0  1  0  0 | 1  0  2 0
oo3oo5/2oo&#x |  1  1 |  * 60  * |  0  2  1  0  0 | 0  1  2 0
.. .x   ..    |  0  2 |  *  * 60 |  0  1  0  1  1 | 0  1  1 1
--------------+-------+----------+----------------+----------
.. o.5/2x.    |  5  0 |  5  0  0 | 12  *  *  *  * | 1  0  1 0
.. ox   ..&#x |  1  2 |  0  2  1 |  * 60  *  *  * | 0  1  1 0
.. ..   xo&#x |  2  1 |  1  2  0 |  *  * 30  *  * | 0  0  2 0
.o3.x   ..    |  0  3 |  0  0  3 |  *  *  * 20  * | 0  1  0 1
.. .x5/2.o    |  0  5 |  0  0  5 |  *  *  *  * 12 | 0  0  1 1
--------------+-------+----------+----------------+----------
o.3o.5/2x.    ♦ 20  0 | 30  0  0 | 12  0  0  0  0 | 1  *  * *
oo3ox   ..&#x ♦  1  3 |  0  3  3 |  0  3  0  1  0 | * 20  * *
.. ox5/2xo&#x ♦  5  5 |  5 10  5 |  1  5  5  0  1 | *  * 12 *
.o3.x5/2.o    ♦  0 30 |  0  0 60 |  0  0  0 20 12 | *  *  * 1