Looks like a compound of a prismatopentahemidecachoron (piphid) plus 10 additional tetrahedra (tet) in pentachoral positions coincident by 2 each.

Incidence matrix according to Dynkin symbol

β3o3o3x

both( . . . . ) | 20 |  3  6 |  3  3  3  6 | 1 1  3 3
----------------+----+-------+-------------+---------
both( . . . x ) |  2 | 30  * |  2  0  0  2 | 1 0  1 2
sefa( β3o . . ) |  2 |  * 60 |  0  1  1  1 | 0 1  1 1
----------------+----+-------+-------------+---------
both( . . o3x ) |  3 |  3  0 | 20  *  *  * | 1 0  0 1
      β3o . .   ♦  3 |  0  3 |  * 20  *  * | 0 1  1 0
sefa( β3o3o . ) |  3 |  0  3 |  *  * 20  * | 0 1  0 1
sefa( β3o . x ) |  4 |  2  2 |  *  *  * 30 | 0 0  1 1
----------------+----+-------+-------------+---------
both( . o3o3x ) ♦  4 |  6  0 |  4  0  0  0 | 5 *  * *
      β3o3o .   ♦  4 |  0 12 |  0  4  4  0 | * 5  * *
      β3o . x   ♦  6 |  3  6 |  0  2  0  3 | * * 10 *
sefa( β3o3o3x ) ♦ 12 | 12 12 |  4  0  4  6 | * *  * 5