As abstract polytope sissidadid is isomorphic to gaddadid, thereby interchanging pentagons and pentagrams resp. replacing sissids by gads, peppies by stappies, and staps by paps.

Incidence matrix according to Dynkin symbol

xo5/2ox5oo&#x   → height = sqrt[(5 sqrt(5)-9)/8] = 0.522056
(sissid || did)

o.5/2o.5o.    | 12  * |  5  5  0 |  5  5  5  0  0 | 1  5  1 0
.o5/2.o5.o    |  * 30 |  0  2  4 |  0  1  4  2  2 | 0  2  2 1
--------------+-------+----------+----------------+----------
x.   .. ..    |  2  0 | 30  *  * |  2  1  0  0  0 | 1  2  0 0
oo5/2oo5oo&#x |  1  1 |  * 60  * |  0  1  2  0  0 | 0  2  1 0
..   .x ..    |  0  2 |  *  * 60 |  0  0  1  1  1 | 0  1  1 1
--------------+-------+----------+----------------+----------
x.5/2o. ..    |  5  0 |  5  0  0 | 12  *  *  *  * | 1  1  0 0
xo   .. ..&#x |  2  1 |  1  2  0 |  * 30  *  *  * | 0  2  0 0
..   ox ..&#x |  1  2 |  0  2  1 |  *  * 60  *  * | 0  1  1 0
.o5/2.x ..    |  0  5 |  0  0  5 |  *  *  * 12  * | 0  1  0 1
..   .x5.o    |  0  5 |  0  0  5 |  *  *  *  * 12 | 0  0  1 1
--------------+-------+----------+----------------+----------
x.5/2o.5o.    ♦ 12  0 | 30  0  0 | 12  0  0  0  0 | 1  *  * *
xo5/2ox ..&#x ♦  5  5 |  5 10  5 |  1  5  5  1  0 | * 12  * *
..   ox5oo&#x ♦  1  5 |  0  5  5 |  0  0  5  0  1 | *  * 12 *
.o5/2.x5.o    ♦  0 30 |  0  0 60 |  0  0  0 12 12 | *  *  * 1