Looks like a compound of a small trisoctachoron (sto) and 16 pairwise coincident tetrahedra (tet) added in pseudo positions. Thus too it is an edge-faceting of the rectified tesseract (rit).

Incidence matrix according to Dynkin symbol

β3o3x *b3o

both( . . .    . ) | 32 |  3  6 |  3  3  6  3 | 1 3 1 3
-------------------+----+-------+-------------+--------
both( . . x    . ) |  2 | 48  * |  2  0  2  0 | 1 2 0 1
sefa( β3o .    . ) |  2 |  * 96 |  0  1  1  1 | 0 1 1 1
-------------------+----+-------+-------------+--------
both( . o3x    . ) |  3 |  3  0 | 32  *  *  * | 1 1 0 0
      β3o .    .   ♦  3 |  0  3 |  * 32  *  * | 0 1 1 0
sefa( β3o3x    . ) |  6 |  3  3 |  *  * 32  * | 0 1 0 1
sefa( β3o . *b3o ) |  3 |  0  3 |  *  *  * 32 | 0 0 1 1
-------------------+----+-------+-------------+--------
both( . o3x *b3o ) ♦  4 |  6  0 |  4  0  0  0 | 8 * * *
      β3o3x    .   ♦ 12 | 12 12 |  4  4  4  0 | * 8 * *
      β3o . *b3o   ♦  4 |  0 12 |  0  4  0  4 | * * 8 *
sefa( β3o3x *b3o ) ♦ 12 |  6 12 |  0  0  4  4 | * * * 8

starting figure: x3o3x *b3o