This polychoron classifies as wild, because each square of the base cube shares its edges with a lacing square and a triangle of an according tutrip each, and that tripple of incident faces would all be corealmic.

Incidence matrix according to Dynkin symbol

"coord-planes squares star" || cube   → sqrt(3)/2 = 0.866025

12 * ♦  2  2  0 | 1  4  1 0 | 2 2 0
 * 8 |  0  3  3 | 0  6  3 3 | 3 3 1
-----+----------+-----------+------
 2 0 | 12  *  * | 1  2  0 0 | 2 1 0
 1 1 |  * 24  * | 0  2  1 0 | 1 2 0
 0 2 |  *  * 12 | 0  2  1 2 | 2 2 1
-----+----------+-----------+------
 4 0 |  4  0  0 | 3  *  * * | 2 0 0
 2 2 |  1  2  1 | * 24  * * | 1 1 0
 1 2 |  0  2  1 | *  * 12 * | 0 2 0
 0 4 |  0  0  4 | *  *  * 6 | 1 0 1
-----+----------+-----------+------
 4 4 |  4  4  4 | 1  4  0 1 | 6 * * cube
 4 4 |  2  8  4 | 0  4  4 0 | * 6 * tutrip
 0 8 |  0  0 12 | 0  0  0 6 | * * 1 cube