Looks like a compound of 2 coincident small rhombated pentachoron (srip), and indeed all but the Grünbaumian elements coincide by pairs. It comes in different forms, either using the cuboctahedral and octahedral places (type A) or the octahedral and triangular prismatic places (type B) for interconnection of the sheets. Type A even splits according to the used 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

x3β3x3o   (type A1)

both( . . . . ) | 60 |  1  2  1  2 |  2  1  1  2  2  1 |  1 2 1  1
----------------+----+-------------+-------------------+----------
both( x . . . ) |  2 | 30  *  *  * |  2  0  1  0  0  0 |  1 2 0  0
both( . . x . ) |  2 |  * 60  *  * |  1  1  0  1  0  0 |  1 1 1  0
sefa( x3β . . ) |  2 |  *  * 30  * |  0  0  1  0  2  0 |  0 2 0  1
sefa( . β3x . ) |  2 |  *  *  * 60 |  0  0  0  1  1  1 |  0 1 1  1
----------------+----+-------------+-------------------+----------
both( x . x . ) |  4 |  2  2  0  0 | 30  *  *  *  *  * |  1 1 0  0
both( . . x3o ) |  3 |  0  3  0  0 |  * 20  *  *  *  * |  1 0 1  0
      x3β . .   ♦  6 |  3  0  3  0 |  *  * 10  *  *  * |  0 2 0  0
      . β3x .   ♦  6 |  0  3  0  3 |  *  *  * 20  *  * |  0 1 1  0
sefa( x3β3x . ) |  4 |  0  0  2  2 |  *  *  *  * 30  * |  0 1 0  1
sefa( . β3x3o ) |  3 |  0  0  0  3 |  *  *  *  *  * 20 |  0 0 1  1
----------------+----+-------------+-------------------+----------
both( x . x3o ) ♦  6 |  3  6  0  0 |  3  2  0  0  0  0 | 10 * *  *
      x3β3x .   ♦ 24 | 12 12 12 12 |  6  0  4  4  6  0 |  * 5 *  *
      . β3x3o   ♦ 12 |  0 12  0 12 |  0  4  0  4  0  4 |  * * 5  *
sefa( x3β3x3o ) ♦  6 |  0  0  3  6 |  0  0  0  0  3  2 |  * * * 10

starting figure: x3x3x3o

β3β3x3o   (type A2)

both( . . . . ) | 60 |  2  2  2 |  1  1  2  4  1 | 2 1  2
----------------+----+----------+----------------+-------
both( . . x . ) |  2 | 60  *  * |  1  0  1  1  0 | 1 1  1
sefa( s3s . . ) |  2 |  * 60  * |  0  1  0  2  0 | 2 0  1
sefa( . β3x . ) |  2 |  *  * 60 |  0  0  1  1  1 | 1 1  1
----------------+----+----------+----------------+-------
both( . . x3o ) |  3 |  3  0  0 | 20  *  *  *  * | 0 1  1
both( s3s . . ) ♦  3 |  0  3  0 |  * 20  *  *  * | 2 0  0
      . β3x .   ♦  6 |  3  0  3 |  *  * 20  *  * | 1 1  0
sefa( β3β3x . ) |  4 |  1  2  1 |  *  *  * 60  * | 1 0  1
sefa( . β3x3o ) |  3 |  0  0  3 |  *  *  *  * 20 | 0 1  1
----------------+----+----------+----------------+-------
      β3β3x .   ♦ 24 | 12 24 12 |  0  8  4 12  0 | 5 *  *
      . β3x3o   ♦ 12 | 12  0 12 |  4  0  4  0  4 | * 5  *
sefa( β3β3x3o ) ♦  6 |  3  3  3 |  1  0  0  3  1 | * * 20

starting figure: x3x3x3o

β3x3o3x   (type B)

both( . . . . ) | 60 |  2  2  2 |  1  2  1  2  1  2 | 1 1  2 1
----------------+----+----------+-------------------+---------
both( . x . . ) |  2 | 60  *  * |  1  1  0  1  0  0 | 1 1  1 0
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( . x3o . ) |  3 |  3  0  0 | 20  *  *  *  *  * | 1 1  0 0
both( . x . x ) |  4 |  2  2  0 |  * 30  *  *  *  * | 1 0  1 0
both( . . o3x ) |  3 |  0  3  0 |  *  * 20  *  *  * | 1 0  0 1
      β3x . .   ♦  6 |  3  0  3 |  *  *  * 20  *  * | 0 1  1 0
sefa( β3x3o . ) |  3 |  0  0  3 |  *  *  *  * 20  * | 0 1  0 1
sefa( β3x . x ) |  4 |  0  2  2 |  *  *  *  *  * 30 | 0 0  1 1
----------------+----+----------+-------------------+---------
both( . x3o3x ) ♦ 12 | 12 12  0 |  4  6  4  0  0  0 | 5 *  * *
      β3x3o .   ♦ 12 | 12  0 12 |  4  0  0  4  4  0 | * 5  * *
      β3x . x   ♦ 12 |  6  6  6 |  0  3  0  2  0  3 | * * 10 *
sefa( β3x3o3x ) ♦ 12 |  0 12 12 |  0  0  4  0  4  6 | * *  * 5

starting figure: x3x3o3x