Looks like the compound of 2 great rhombated icositetrachora (grico), and indeed all but the Grünbaumian elements coincide by pairs.

Incidence matrix according to Dynkin symbol

β3x4x3x

both( . . . . ) | 1152 |   1   1   1   1 |   1   1   1   1   1   1 |  1  1  1  1
----------------+------+-----------------+-------------------------+------------
both( . x . . ) |    2 | 576   *   *   * |   1   1   0   1   0   0 |  1  1  1  0
both( . . x . ) |    2 |   * 576   *   * |   1   0   1   0   1   0 |  1  1  0  1
both( . . . x ) |    2 |   *   * 576   * |   0   1   1   0   0   1 |  1  0  1  1
sefa( β3x . . ) |    2 |   *   *   * 576 |   0   0   0   1   1   1 |  0  1  1  1
----------------+------+-----------------+-------------------------+------------
both( . x4x . ) |    8 |   4   4   0   0 | 144   *   *   *   *   * |  1  1  0  0
both( . x . x ) |    4 |   2   0   2   0 |   * 288   *   *   *   * |  1  0  1  0
both( . . x3x ) |    6 |   0   3   3   0 |   *   * 192   *   *   * |  1  0  0  1
      β3x . .   ♦    6 |   3   0   0   3 |   *   *   * 192   *   * |  0  1  1  0
sefa( β3x4x . ) |    8 |   0   4   0   4 |   *   *   *   * 144   * |  0  1  0  1
sefa( β3x 2 x ) |    4 |   0   0   2   2 |   *   *   *   *   * 288 |  0  0  1  1 
----------------+------+-----------------+-------------------------+------------
both( . x4x3x ) ♦   48 |  24  24  24   0 |   6  12   8   0   0   0 | 24  *  *  *
      β3x4x .   ♦   48 |  24  24   0  24 |   6   0   0   8   6   0 |  * 24  *  *
      β3x 2 x   ♦   12 |   6   0   6   6 |   0   3   0   2   0   3 |  *  * 96  *
sefa( β3x4x3x ) ♦   48 |   0  24  24  24 |   0   0   8   0   6  12 |  *  *  * 24

starting figure: x3x4x3x