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-axes edge star" || cube   → height = 1/sqrt(2) = 0.707107

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