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

Incidence matrix according to Dynkin symbol

β3x3x3x

both( . . . . ) | 120 |  1  1  1  1 |  1  1  1  1  1  1 | 1 1  1 1
----------------+-----+-------------+-------------------+---------
both( . x . . ) |   2 | 60  *  *  * |  1  1  0  1  0  0 | 1 1  1 0
both( . . x . ) |   2 |  * 60  *  * |  1  0  1  0  1  0 | 1 1  0 1
both( . . . x ) |   2 |  *  * 60  * |  0  1  1  0  0  1 | 1 0  1 1
sefa( β3x . . ) |   2 |  *  *  * 60 |  0  0  0  1  1  1 | 0 1  1 1
----------------+-----+-------------+-------------------+---------
both( . x3x . ) |   6 |  3  3  0  0 | 20  *  *  *  *  * | 1 1  0 0
both( . x . x ) |   4 |  2  0  2  0 |  * 30  *  *  *  * | 1 0  1 0
both( . . x3x ) |   6 |  0  3  3  0 |  *  * 20  *  *  * | 1 0  0 1
      β3x . .   ♦   6 |  3  0  0  3 |  *  *  * 20  *  * | 0 1  1 0
sefa( β3x3x . ) |   6 |  0  3  0  3 |  *  *  *  * 20  * | 0 1  0 1
sefa( β3x . x ) |   4 |  0  0  2  2 |  *  *  *  *  * 30 | 0 0  1 1
----------------+-----+-------------+-------------------+---------
both( . x3x3x ) ♦  24 | 12 12 12  0 |  4  6  4  0  0  0 | 5 *  * *
      β3x3x .   ♦  24 | 12 12  0 12 |  4  0  0  4  4  0 | * 5  * *
      β3x . x   ♦  12 |  6  0  6  6 |  0  3  0  2  0  3 | * * 10 *
sefa( β3x3x3x ) ♦  24 |  0 12 12 12 |  0  0  4  0  4  6 | * *  * 5

starting figure: x3x3x3x