Looks like a compound of 2 coincident small rhombated hexacosachora (srix). Indeed all but the Grünbaumian elements coincide by pairs. It occurs in different types: Type A has coincident pairs of pentagonal prisms (pip), while type B has coincident pairs of cuboctahedra (co). Type A even splits according to the used version of the Grünbaumian doubly covered cuboctahedral cells (2co): in type A1 all cuboctahedral triangles will be replaced by {6/2}, in type A2 only half of those.

Incidence matrix according to Dynkin symbol

x3β3x5o   (type A1)

both( . . . . ) | 7200 |    1    2    1    2 |    2    1    1    2    2    1 |   1   2   1   1
----------------+------+---------------------+-------------------------------+----------------
both( x . . . ) |    2 | 3600    *    *    * |    2    0    1    0    0    0 |   1   2   0   0
both( . . x . ) |    2 |    * 7200    *    * |    1    1    0    1    0    0 |   1   1   1   0
sefa( x3β . . ) |    2 |    *    * 3600    * |    0    0    1    0    2    0 |   0   2   0   1
sefa( . β3x . ) |    2 |    *    *    * 7200 |    0    0    0    1    1    1 |   0   1   1   1
----------------+------+---------------------+-------------------------------+----------------
both( x . x . ) |    4 |    2    2    0    0 | 3600    *    *    *    *    * |   1   1   0   0
both( . . x5o ) |    5 |    0    5    0    0 |    * 1440    *    *    *    * |   1   0   1   0
      x3β . .   ♦    6 |    3    0    3    0 |    *    * 1200    *    *    * |   0   2   0   0
      . β3x .   ♦    6 |    0    3    0    3 |    *    *    * 2400    *    * |   0   1   1   0
sefa( x3β3x . ) |    4 |    0    0    2    2 |    *    *    *    * 3600    * |   0   1   0   1
sefa( . β3x5o ) |    5 |    0    0    0    5 |    *    *    *    *    * 1440 |   0   0   1   1
----------------+------+---------------------+-------------------------------+----------------
both( x . x5o ) ♦   10 |    5   10    0    0 |    5    2    0    0    0    0 | 720   *   *   *
      x3β3x .   ♦   24 |   12   12   12   12 |    6    0    4    4    6    0 |   * 600   *   *
      . β3x5o   ♦   60 |    0   60    0   60 |    0   12    0   20    0   12 |   *   * 120   *
sefa( x3β3x5o ) ♦   10 |    0    0    5   10 |    0    0    0    0    5    2 |   *   *   * 720

starting figure: x3x3x5o

β3β3x5o   (type A2)

both( . . . . ) | 7200 |    2    2    2 |    1    1    2    4    1 |   2   1    2
----------------+------+----------------+--------------------------+-------------
both( . . x . ) |    2 | 7200    *    * |    1    0    1    1    0 |   1   1    1
sefa( s3s . . ) |    2 |    * 7200    * |    0    1    0    2    0 |   2   0    1
sefa( . β3x . ) |    2 |    *    * 7200 |    0    0    1    1    1 |   1   1    1
----------------+------+----------------+--------------------------+-------------
both( . . x5o ) |    5 |    5    0    0 | 1440    *    *    *    * |   0   1    1
both( s3s . . ) ♦    3 |    0    3    0 |    * 2400    *    *    * |   2   0    0
      . β3x .   ♦    6 |    3    0    3 |    *    * 2400    *    * |   1   1    0
sefa( β3β3x . ) |    4 |    1    2    1 |    *    *    * 7200    * |   1   0    1
sefa( . β3x5o ) |    5 |    0    0    5 |    *    *    *    * 1440 |   0   1    1
----------------+------+----------------+--------------------------+-------------
      β3β3x .   ♦   24 |   12   24   12 |    0    8    4   12    0 | 600   *    *
      . β3x5o   ♦   60 |   60    0   60 |   12    0   20    0   12 |   * 120    *
sefa( β3β3x5o ) ♦   10 |    5    5    5 |    1    0    0    5    1 |   *   * 1440

starting figure: x3x3x5o

x3o3x5β   (type B)

both( . . . . ) | 7200 |    2    2    2 |    1    2    1    2    2    1 |   1   2   1   1
----------------+------+----------------+-------------------------------+----------------
both( x . . . ) |    2 | 7200    *    * |    1    1    0    0    1    0 |   1   1   0   1
both( . . x . ) |    2 |    * 7200    * |    0    1    1    1    0    0 |   1   1   1   0
sefa( . . x5β ) |    2 |    *    * 7200 |    0    0    0    1    1    1 |   0   1   1   1
----------------+------+----------------+-------------------------------+----------------
both( x3o . . ) |    3 |    3    0    0 | 2400    *    *    *    *    * |   1   0   0   1
both( x . x . ) |    4 |    2    2    0 |    * 3600    *    *    *    * |   1   1   0   0
both( . o3x . ) |    3 |    0    3    0 |    *    * 2400    *    *    * |   1   0   1   0
      . . x5β   ♦   10 |    0    5    5 |    *    *    * 1440    *    * |   0   1   1   0
sefa( x 2 x5β ) |    4 |    2    0    2 |    *    *    *    * 3600    * |   0   1   0   1
sefa( . o3x5β ) |    3 |    0    0    3 |    *    *    *    *    * 2400 |   0   0   1   1
----------------+------+----------------+-------------------------------+----------------
both( x3o3x . ) ♦   12 |   12   12    0 |    4    6    4    0    0    0 | 600   *   *   *
      x 2 x5β   ♦   20 |   10   10   10 |    0    5    0    2    5    0 |   * 720   *   *
      . o3x5β   ♦   60 |    0   60   60 |    0    0   20   12    0   20 |   *   * 120   *
sefa( x3o3x5β ) ♦   12 |   12    0   12 |    4    0    0    0    6    4 |   *   *   * 600

starting figure: x3o3x5x