The blend of stopper and stapper does blend out all triangles, pentagons, and pentagrams, leaving just a mere cube then.

As abstract polytope stopper is automorph, thereby interchanging the roles of pentagons and pentagrams.

Incidence matrix

2 * * * | 2 2 0 0 0 0 0 0 | 1 2 1 0 0 0  [3,5/2,5/4,5/2]
* 4 * * | 1 0 1 1 1 0 0 0 | 1 1 0 1 1 0  [3,4,4,5/2]
* * 2 * | 0 2 0 0 0 2 0 0 | 0 1 2 0 0 1  [3,5,5/3,5]/0
* * * 4 | 0 0 0 0 1 1 1 1 | 0 0 1 1 1 1  [3,4/3,4/3,5]/0
--------+-----------------+------------
1 1 0 0 | 4 * * * * * * * | 1 1 0 0 0 0
1 0 1 0 | * 4 * * * * * * | 0 1 1 0 0 0
0 2 0 0 | * * 2 * * * * * | 1 0 0 1 0 0  at {3}
0 2 0 0 | * * * 2 * * * * | 0 1 0 0 1 0  at {5/2}
0 1 0 1 | * * * * 4 * * * | 0 0 0 1 1 0
0 0 1 1 | * * * * * 4 * * | 0 0 1 0 0 1
0 0 0 2 | * * * * * * 2 * | 0 0 0 0 1 1  at {3}
0 0 0 2 | * * * * * * * 2 | 0 0 1 1 0 0  at {5}
--------+-----------------+------------
1 2 0 0 | 2 0 1 0 0 0 0 0 | 2 * * * * *  {3}
2 2 1 0 | 2 2 0 1 0 0 0 0 | * 2 * * * *  {5/2}
1 0 2 2 | 0 2 0 0 0 2 0 1 | * * 2 * * *  {5}
0 2 0 2 | 0 0 1 0 2 0 0 1 | * * * 2 * *  {4}
0 2 0 2 | 0 0 0 1 2 0 1 0 | * * * * 2 *  {4}
0 0 1 2 | 0 0 0 0 0 2 1 0 | * * * * * 2  {3}