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

Incidence matrix according to Dynkin symbol

x3β3x3x

both( . . . . ) | 120 |  1  1  1  1  1 |  1  1  1  1  1  1  1  1 |  1 1  1 1  1
----------------+-----+----------------+-------------------------+-------------
both( x . . . ) |   2 | 60  *  *  *  * |  1  1  0  1  0  0  0  0 |  1 1  1 0  0
both( . . x . ) |   2 |  * 60  *  *  * |  1  0  1  0  1  0  0  0 |  1 1  0 1  0
both( . . . x ) |   2 |  *  * 60  *  * |  0  1  1  0  0  0  1  1 |  1 0  1 1  1
sefa( x3β . . ) |   2 |  *  *  * 60  * |  0  0  0  1  0  1  1  0 |  0 1  1 0  1
sefa( . β3x . ) |   2 |  *  *  *  * 60 |  0  0  0  0  1  1  0  1 |  0 1  0 1  1
----------------+-----+----------------+-------------------------+-------------
both( x . x . ) |   4 |  2  2  0  0  0 | 30  *  *  *  *  *  *  * |  1 1  0 0  0
both( x . . x ) |   4 |  2  0  2  0  0 |  * 30  *  *  *  *  *  * |  1 0  1 0  0
both( . . x3x ) |   6 |  0  3  3  0  0 |  *  * 20  *  *  *  *  * |  1 0  0 1  0
      x3β . .   ♦   6 |  3  0  0  3  0 |  *  *  * 20  *  *  *  * |  0 1  1 0  0
      . β3x .   ♦   6 |  0  3  0  0  3 |  *  *  *  * 20  *  *  * |  0 1  0 1  0
sefa( x3β3x . ) |   4 |  0  0  0  2  2 |  *  *  *  *  * 30  *  * |  0 1  0 0  1
sefa( x3β . x ) |   4 |  0  0  2  2  0 |  *  *  *  *  *  * 30  * |  0 0  1 0  1
sefa( . β3x3x ) |   6 |  0  0  3  0  3 |  *  *  *  *  *  *  * 20 |  0 0  0 1  1
----------------+-----+----------------+-------------------------+-------------
both( x . x3x ) ♦  12 |  6  6  6  0  0 |  3  3  2  0  0  0  0  0 | 10 *  * *  *
      x3β3x .   ♦  24 | 12 12  0 12 12 |  6  0  0  4  4  6  0  0 |  * 5  * *  *
      x3β . x   ♦  12 |  6  0  6  6  0 |  0  3  0  2  0  0  3  0 |  * * 10 *  *
      . β3x3x   ♦  24 |  0 12 12  0 12 |  0  0  4  0  4  0  0  4 |  * *  * 5  *
sefa( x3β3x3x ) ♦  12 |  0  0  6  6  6 |  0  0  0  0  0  3  3  2 |  * *  * * 10

starting figure: x3x3x3x

β3β3x3x

both( . . . . ) | 120 |  1  1   2  1 |  1  1  1  2  2  1 | 1  1 1  1
----------------+-----+--------------+-------------------+----------
both( . . x . ) |   2 | 60  *   *  * |  1  0  1  1  0  0 | 1  0 1  1
both( . . . x ) |   2 |  * 60   *  * |  1  0  0  0  2  1 | 0  1 1  2
sefa( s3s . . ) |   2 |  *  * 120  * |  0  1  0  1  1  0 | 1  1 0  1
sefa( . β3x . ) |   2 |  *  *   * 60 |  0  0  1  1  0  1 | 1  0 1  1
----------------+-----+--------------+-------------------+----------
both( . . x3x ) |   6 |  3  3   0  0 | 20  *  *  *  *  * | 0  0 1  1
both( s3s . . ) ♦   3 |  0  0   3  0 |  * 40  *  *  *  * | 1  1 0  0
      . β3x .   ♦   6 |  3  0   0  3 |  *  * 20  *  *  * | 1  0 1  0
sefa( β3β3x . ) |   4 |  1  0   2  1 |  *  *  * 60  *  * | 1  0 0  1
sefa( s3s 2 x ) |   4 |  0  2   2  0 |  *  *  *  * 60  * | 0  1 0  1
sefa( . β3x3x ) |   6 |  0  3   0  3 |  *  *  *  *  * 20 | 0  0 1  1
----------------+-----+--------------+-------------------+----------
      β3β3x .   ♦  24 | 12  0  24 12 |  0  8  4 12  0  0 | 5  * *  *
both( s3s 2 x ) ♦   6 |  0  3   6  0 |  0  2  0  0  3  0 | * 20 *  *
      . β3x3x   ♦  24 | 12 12   0 12 |  4  0  4  0  0  4 | *  * 5  *
sefa( β3β3x3x ) ♦  12 |  3  6   6  3 |  1  0  0  3  3  1 | *  * * 20

starting figure: x3x3x3x