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

Incidence matrix according to Dynkin symbol

xo5ox5/2oo&#x   → height = sqrt[(3 sqrt(5)-1)/8] = 0.844704
(gad || did)

o.5o.5/2o.    | 12  * |  5  5  0 |  5  5  5  0  0 | 1  5  1 0
.o5.o5/2.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
oo5oo5/2oo&#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.5o.   ..    |  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.x   ..    |  0  5 |  0  0  5 |  *  *  * 12  * | 0  1  0 1
.. .x5/2.o    |  0  5 |  0  0  5 |  *  *  *  * 12 | 0  0  1 1
--------------+-------+----------+----------------+----------
x.5o.5/2o.    ♦ 12  0 | 30  0  0 | 12  0  0  0  0 | 1  *  * *
xo5ox   ..&#x ♦  5  5 |  5 10  5 |  1  5  5  1  0 | * 12  * *
.. ox5/2oo&#x ♦  1  5 |  0  5  5 |  0  0  5  0  1 | *  * 12 *
.o5.x5/2.o    ♦  0 30 |  0  0 60 |  0  0  0 12 12 | *  *  * 1