Looks like the compound of 2 coincident small rhombated icositetrachora (srico) and 192 additional triangular prisms (trip), arranged such that the total of 384 prisms coincide by 4 each.

Incidence matrix according to Dynkin symbol

x3β4β3o

both( . . . . ) | 576 |   1   1    4   2 |  1   2   1   4   2   3 |  2  1  1   3
----------------+-----+------------------+------------------------+-------------
both( x . . . ) |   2 | 288   *    *   * |  1   0   0   2   2   0 |  2  1  0   2
sefa( x3β . . ) |   2 |   * 288    *   * |  1   0   0   2   0   0 |  2  0  0   1
sefa( . s4s . ) |   2 |   *   * 1152   * |  0   1   0   1   0   1 |  1  0  1   1
sefa( . . β3o ) |   2 |   *   *    * 576 |  0   0   1   0   1   1 |  0  1  1   1
----------------+-----+------------------+------------------------+-------------
      x3β . .   ♦   6 |   3   3    0   0 | 96   *   *   *   *   * |  2  0  0   0
both( . s4s . ) ♦   4 |   0   0    4   0 |  * 288   *   *   *   * |  1  0  1   0
      . . β3o   ♦   3 |   0   0    0   3 |  *   * 192   *   *   * |  0  1  1   0
sefa( x3β4β . ) |   4 |   1   1    2   0 |  *   *   * 576   *   * |  1  0  0   1
sefa( x . β3o ) |   4 |   2   0    0   2 |  *   *   *   * 288   * |  0  1  0   1
sefa( . β4β3o ) |   3 |   0   0    2   1 |  *   *   *   *   * 576 |  0  0  1   1
----------------+-----+------------------+------------------------+-------------
      x3β4β .   ♦  48 |  24  24   48   0 |  8  12   0  24   0   0 | 24  *  *   *
      x . β3o   ♦   6 |   3   0    0   0 |  0   0   2   0   3   0 |  * 96  *   *
      . β4β3o   ♦  24 |   0   0   48  24 |  0  12   8   0   0  24 |  *  * 24   *
sefa( x3β4β3o ) ♦   6 |   2   1    4   2 |  0   0   0   2   1   2 |  *  *  * 288

starting figure: x3x4x3o