Looks like a compound of 2 coincident great rhombated tesseracts (grit).

Incidence matrix according to Dynkin symbol

β3x3x4x

both( . . . . ) | 384 |   1   1   1   1 |  1  1  1  1  1  1 | 1  1  1 1
----------------+-----+-----------------+-------------------+----------
both( . x . . ) |   2 | 192   *   *   * |  1  1  0  1  0  0 | 1  1  1 0
both( . . x . ) |   2 |   * 192   *   * |  1  0  1  0  1  0 | 1  1  0 1
both( . . . x ) |   2 |   *   * 192   * |  0  1  1  0  0  1 | 1  0  1 1
sefa( β3x . . ) |   2 |   *   *   * 192 |  0  0  0  1  1  1 | 0  1  1 1
----------------+-----+-----------------+-------------------+----------
both( . x3x . ) |   6 |   3   3   0   0 | 64  *  *  *  *  * | 1  1  0 0
both( . x . x ) |   4 |   2   0   2   0 |  * 96  *  *  *  * | 1  0  1 0
both( . . x4x ) |   8 |   0   4   4   0 |  *  * 48  *  *  * | 1  0  0 1
      β3x . .   ♦   6 |   3   0   0   3 |  *  *  * 64  *  * | 0  1  1 0
sefa( β3x3x . ) |   6 |   0   3   0   3 |  *  *  *  * 64  * | 0  1  0 1
sefa( β3x 2 x ) |   4 |   0   0   2   2 |  *  *  *  *  * 96 | 0  0  1 1
----------------+-----+-----------------+-------------------+----------
both( . x3x4x ) ♦  48 |  24  24  24   0 |  8 12  6  0  0  0 | 8  *  * *
      β3x3x .   ♦  24 |  12  12   0  12 |  4  0  0  4  4  0 | * 16  * *
      β3x 2 x   ♦  12 |   6   0   6   6 |  0  3  0  2  0  3 | *  * 32 *
sefa( β3x3x4x ) ♦  48 |   0  24  24  24 |  0  0  6  0  8 12 | *  *  * 8

starting figure: x3x3x4x