Looks like a compound of a small hexacosafaceted prismatodishecatonicosachoron (six fipady) and 1200 tetrahedra (tet). Those tetrahedra come within coincident pairs at corresponding pseudo-cell positions.

Incidence matrix according to Dynkin symbol

β3o3o5x

both( . . . . ) | 2400 |    3    6 |    3    3    3    6 |   1   1    3   3
----------------+------+-----------+---------------------+-----------------
both( . . . x ) |    2 | 3600    * |    2    0    0    2 |   1   0    1   2
sefa( β3o . . ) |    2 |    * 7200 |    0    1    1    1 |   0   1    1   1
----------------+------+-----------+---------------------+-----------------
both( . . o5x ) |    5 |    5    0 | 1440    *    *    * |   1   0    0   1
      β3o . .   ♦    3 |    0    3 |    * 2400    *    * |   0   1    1   0
sefa( β3o3o . ) |    3 |    0    3 |    *    * 2400    * |   0   1    0   1
sefa( β3o 2 x ) |    4 |    2    2 |    *    *    * 3600 |   0   0    1   1
----------------+------+-----------+---------------------+-----------------
both( . o3o5x ) ♦   20 |   30    0 |   12    0    0    0 | 120   *    *   *
      β3o3o .   ♦    4 |    0   12 |    0    4    4    0 |   * 600    *   *
      β3o 2 x   ♦    6 |    3    6 |    0    2    0    3 |   *   * 1200   *
sefa( β3o3o5x ) ♦   60 |   60   60 |   12    0   20   30 |   *   *    * 120

starting figure: x3o3o5x