As abstract polytope is isomorphe to ikaid, thereby replacing pentagrams by pentagons, resp. gike by ike, stappy by peppy, and gid by id.

Incidence matrix according to Dynkin symbol

xo3ox5/2oo&#x   → height = (1+sqrt(5))/4 = 0.809017
(gike || gid)

o.3o.5/2o.    | 12  * ♦  5  5  0 |  5  5  5  0  0 | 1  5  1 0
.o3.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
oo3oo5/2oo&#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.3o.   ..    |  3  0 |  3  0  0 | 20  *  *  *  * | 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
.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
--------------+-------+----------+----------------+----------
x.3o.5/2o.    ♦ 12  0 | 30  0  0 | 20  0  0  0  0 | 1  *  * *
xo3ox   ..&#x ♦  3  3 |  3  6  3 |  1  3  3  1  0 | * 20  * *
.. ox5/2oo&#x ♦  1  5 |  0  5  5 |  0  0  5  0  1 | *  * 12 *
.o3.x5/2.o    ♦  0 30 |  0  0 60 |  0  0  0 20 12 | *  *  * 1