Looks like a compound of 2 prismatorhombated hexacosichora (prix), 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 decagonal prisms (dip) as Grünbaumian cells, while in type B additionally the triangular prisms (trip) come in coincident pairs.

Incidence matrix according to Dynkin symbol

x3β3x5x   (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    1    0    0    0    0 |   1   1    1   0   0
both( . . x . ) |     2 |    * 7200    *    *    * |    1    0    1    0    1    0    0    0 |   1   1    0   1   0
both( . . . x ) |     2 |    *    * 7200    *    * |    0    1    1    0    0    0    1    1 |   1   0    1   1   1
sefa( x3β . . ) |     2 |    *    *    * 7200    * |    0    0    0    1    0    1    1    0 |   0   1    1   0   1
sefa( . β3x . ) |     2 |    *    *    *    * 7200 |    0    0    0    0    1    1    0    1 |   0   1    0   1   1
----------------+-------+--------------------------+-----------------------------------------+---------------------
both( x . x . ) |     4 |    2    2    0    0    0 | 3600    *    *    *    *    *    *    * |   1   1    0   0   0
both( x . . x ) |     4 |    2    0    2    0    0 |    * 3600    *    *    *    *    *    * |   1   0    1   0   0
both( . . x5x ) |    10 |    0    5    5    0    0 |    *    * 1440    *    *    *    *    * |   1   0    0   1   0
      x3β . .   ♦     6 |    3    0    0    3    0 |    *    *    * 2400    *    *    *    * |   0   1    1   0   0
      . β3x .   ♦     6 |    0    3    0    0    3 |    *    *    *    * 2400    *    *    * |   0   1    0   1   0
sefa( x3β3x . ) |     4 |    0    0    0    2    2 |    *    *    *    *    * 3600    *    * |   0   1    0   0   1
sefa( x3β 2 x ) |     4 |    0    0    2    2    0 |    *    *    *    *    *    * 3600    * |   0   0    1   0   1
sefa( . β3x5x ) |    10 |    0    0    5    0    5 |    *    *    *    *    *    *    * 1440 |   0   0    0   1   1
----------------+-------+--------------------------+-----------------------------------------+---------------------
both( x . x5x ) ♦    20 |   10   10   10    0    0 |    5    5    2    0    0    0    0    0 | 720   *    *   *   *
      x3β3x .   ♦    24 |   12   12    0   12   12 |    6    0    0    4    4    6    0    0 |   * 600    *   *   *
      x3β 2 x   ♦    12 |    6    0    6    6    0 |    0    3    0    2    0    0    3    0 |   *   * 1200   *   *
      . β3x5x   ♦   120 |    0   60   60    0   60 |    0    0   12    0   20    0    0   12 |   *   *    * 120   *
sefa( x3β3x5x ) ♦    20 |    0    0   10   10   10 |    0    0    0    0    0    5    5    2 |   *   *    *   * 720

starting figure: x3x3x5x

β3β3x5x   (type B)

both( . . . . ) | 14400 |    1    1     2    1 |    1    1    1    2    2    1 |   1    1   1    2
----------------+-------+----------------------+-------------------------------+------------------
both( . . x . ) |     2 | 7200    *     *    * |    1    0    1    1    0    0 |   1    0   1    1
both( . . . x ) |     2 |    * 7200     *    * |    1    0    0    0    2    1 |   0    1   1    2
sefa( s3s . . ) |     2 |    *    * 14400    * |    0    1    0    1    1    0 |   1    1   0    1
sefa( . β3x . ) |     2 |    *    *     * 7200 |    0    0    1    1    0    1 |   1    0   1    1
----------------+-------+----------------------+-------------------------------+------------------
both( . . x5x ) |    10 |    5    5     0    0 | 1440    *    *    *    *    * |   0    0   1    1
both( s3s . . ) ♦     3 |    0    0     3    0 |    * 4800    *    *    *    * |   1    1   0    0
      . β3x .   ♦     6 |    3    0     0    3 |    *    * 2400    *    *    * |   1    0   1    0
sefa( β3β3x . ) |     4 |    1    0     2    1 |    *    *    * 7200    *    * |   1    0   0    1
sefa( s3s 2 x ) |     4 |    0    2     2    0 |    *    *    *    * 7200    * |   0    1   0    1
sefa( . β3x5x ) |    10 |    0    5     0    5 |    *    *    *    *    * 1440 |   0    0   1    1
----------------+-------+----------------------+-------------------------------+------------------
      β3β3x .   ♦    24 |   12    0    24   12 |    0    8    4   12    0    0 | 600    *   *    *
both( s3s 2 x ) ♦     6 |    0    3     6    0 |    0    2    0    0    3    0 |   * 2400   *    *
      . β3x5x   ♦   120 |   60   60     0   60 |   12    0   20    0    0   12 |   *    * 120    *
sefa( β3β3x5x ) ♦    20 |    5   10    10    5 |    1    0    0    5    5    1 |   *    *   * 1440

starting figure: x3x3x5x