Looks like a compound of 2 prismatorhombated hecatonicosachora (prahi), and indeed all but the Grünbaumian elements coincide by pairs. It comes in different types depending on which cells are Grünbaumian: type A uses all but the hexagonal prisms (hip) as Grünbaumian cells, while in type B the pentagonal prisms (pip) also come in coincident pairs.

Incidence matrix according to Dynkin symbol

x3x3β5x   (type A)

both( . . . . ) | 14400 |    1    1    1    1    1 |    1    1    1    1    1    1    1    1 |    1   1   1   1    1
----------------+-------+--------------------------+-----------------------------------------+----------------------
both( x . . . ) |     2 | 7200    *    *    *    * |    1    1    0    0    0    1    1    0 |    1   1   1   0    1
both( . x . . ) |     2 |    * 7200    *    *    * |    1    0    1    1    0    0    0    0 |    1   1   0   1    0
both( . . . x ) |     2 |    *    * 7200    *    * |    0    1    1    0    1    0    0    0 |    1   0   1   1    0
sefa( . x3β . ) |     2 |    *    *    * 7200    * |    0    0    0    1    0    1    0    1 |    0   1   0   1    1
sefa( . . β5x ) |     2 |    *    *    *    * 7200 |    0    0    0    0    1    0    1    1 |    0   0   1   1    1
----------------+-------+--------------------------+-----------------------------------------+----------------------
both( x3x . . ) |     6 |    3    3    0    0    0 | 2400    *    *    *    *    *    *    * |    1   1   0   0    0
both( x . . x ) |     4 |    2    0    2    0    0 |    * 3600    *    *    *    *    *    * |    1   0   1   0    0
both( . x . x ) |     4 |    0    2    2    0    0 |    *    * 3600    *    *    *    *    * |    1   0   0   1    0
      . x3β .   ♦     6 |    0    3    0    3    0 |    *    *    * 2400    *    *    *    * |    0   1   0   1    0
      . . β5x   ♦    10 |    0    0    5    0    5 |    *    *    *    * 1440    *    *    * |    0   0   1   1    0
sefa( x3x3β . ) |     6 |    3    0    0    3    0 |    *    *    *    *    * 2400    *    * |    0   1   0   0    1
sefa( x 2 β5x ) |     4 |    2    0    0    0    2 |    *    *    *    *    *    * 3600    * |    0   0   1   0    1
sefa( . x3β5x ) |     4 |    0    0    0    2    2 |    *    *    *    *    *    *    * 3600 |    0   0   0   1    1
----------------+-------+--------------------------+-----------------------------------------+----------------------
both( x3x . x ) ♦    12 |    6    6    6    0    0 |    2    3    3    0    0    0    0    0 | 1200   *   *   *    *
      x3x3β .   ♦    24 |   12   12    0   12    0 |    4    0    0    4    0    4    0    0 |    * 600   *   *    *
      x 2 β5x   ♦    20 |   10    0   10    0   10 |    0    5    0    0    2    0    5    0 |    *   * 720   *    *
      . x3β5x   ♦   120 |    0   60   60   60   60 |    0    0   30   20   12    0    0   30 |    *   *   * 120    *
sefa( x3x3β5x ) ♦    12 |    6    0    0    6    6 |    0    0    0    0    0    2    3    3 |    *   *   *   * 1200

starting figure: x3x3x5x

x3x3β5β   (type B)
both( . . . . ) | 14400 |    1    1    1     2 |    1    1    1    1    2    2 |   1    1   1    2
----------------+-------+----------------------+-------------------------------+------------------
both( x . . . ) |     2 | 7200    *    *     * |    1    0    0    1    2    0 |   1    1   0    2
both( . x . . ) |     2 |    * 7200    *     * |    1    1    0    0    0    1 |   1    0   1    1
sefa( . x3β . ) |     2 |    *    * 7200     * |    0    1    0    1    0    1 |   1    0   1    1
sefa( . . s5s ) |     2 |    *    *    * 14400 |    0    0    1    0    1    1 |   0    1   1    1
----------------+-------+----------------------+-------------------------------+------------------
both( x3x . . ) |     6 |    3    3    0     0 | 2400    *    *    *    *    * |   1    0   0    1
      . x3β .   ♦     6 |    0    3    3     0 |    * 2400    *    *    *    * |   1    0   1    0
both( . . s5s ) ♦     5 |    0    0    0     5 |    *    * 2880    *    *    * |   0    1   1    0
sefa( x3x3β . ) |     6 |    3    0    3     0 |    *    *    * 2400    *    * |   1    0   0    1
sefa( x 2 s5s ) |     4 |    2    0    0     2 |    *    *    *    * 7200    * |   0    1   0    1
sefa( . x3β5β ) |     4 |    0    1    1     2 |    *    *    *    *    * 7200 |   0    0   1    1
----------------+-------+----------------------+-------------------------------+------------------
      x3x3β .   ♦    24 |   12   12   12     0 |    4    4    0    4    0    0 | 600    *   *    *
both( x 2 s5s ) ♦    10 |    5    0    0    10 |    0    0    2    0    5    0 |   * 1440   *    *
      . x3β5β   ♦   120 |    0   60   60   120 |    0   20   24    0    0   60 |   *    * 120    *
sefa( x3x3β5β ) ♦    12 |    6    3    3     6 |    1    0    0    1    3    3 |   *    *   * 2400

starting figure: x3x3x5x