Acronym ...
Name three squaf blend,
"thah-squares star" atop cube
Circumradius sqrt[(4+sqrt(2))/7] = 0.879465
Confer "coord-axes edge star" || cube   "coord-planes square star" || cube  

Incidence matrix according to Dynkin symbol

"thah-squares star" || cube   → height = sqrt[2 sqrt(2)-1]/2 = 0.676097

6 * |  4  4  0 | 2  8  4 0 | 4  4 0
* 8 |  0  3  3 | 0  3  6 3 | 3  3 1
----+----------+-----------+-------
2 0 | 12  *  * | 1  2  0 0 | 2  1 0
1 1 |  * 24  * | 0  2  2 0 | 2  2 0
0 2 |  *  * 12 | 0  0  2 2 | 2  1 1
----+----------+-----------+-------
4 0 |  4  0  0 | 3  *  * * | 2  0 0
2 1 |  1  2  0 | * 24  * * | 1  1 0
1 2 |  0  2  1 | *  * 24 * | 1  1 0
0 4 |  0  0  4 | *  *  * 6 | 1  0 1
----+----------+-----------+-------
4 4 |  4  8  4 | 1  4  4 1 | 6  * * squap
2 2 |  1  4  1 | 0  2  2 0 | * 12 * tet
0 8 |  0  0 12 | 0  0  0 6 | *  * 1 cube

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