Looks like a compound of 2 coincident small rhombated pentachoron (srip) plus 20 more triangular prisms (trip), which coincide with those of the srips by 4 each.

Incidence matrix according to Dynkin symbol

x3β3β3o

both( . . . . ) | 60 |  1  1   4  2 |  1  2  1  4  2  3 | 2  1 1  3
----------------+----+--------------+-------------------+----------
both( x . . . ) |  2 | 30  *   *  * |  1  0  0  2  2  0 | 2  1 0  2
sefa( x3β . . ) |  2 |  * 30   *  * |  1  0  0  2  0  0 | 2  0 0  1
sefa( . s3s . ) |  2 |  *  * 120  * |  0  1  0  1  0  1 | 1  0 1  1
sefa( . . β3o ) |  2 |  *  *   * 60 |  0  0  1  0  1  1 | 0  1 1  1
----------------+----+--------------+-------------------+----------
      x3β . .   ♦  6 |  3  3   0  0 | 10  *  *  *  *  * | 2  0 0  0
both( . s3s . ) ♦  3 |  0  0   3  0 |  * 40  *  *  *  * | 1  0 1  0
      . . β3o   ♦  3 |  0  0   0  3 |  *  * 20  *  *  * | 0  1 1  0
sefa( x3β3β . ) |  4 |  1  1   2  0 |  *  *  * 60  *  * | 1  0 0  1
sefa( x 2 β3o ) |  4 |  2  0   0  2 |  *  *  *  * 30  * | 0  1 0  1
sefa( . β3β3o ) |  3 |  0  0   2  1 |  *  *  *  *  * 60 | 0  0 1  1
----------------+----+--------------+-------------------+----------
      x3β3β .   ♦ 24 | 12 12  24  0 |  4  8  0 12  0  0 | 5  * *  *
      x 2 β3o   ♦  6 |  3  0   0  6 |  0  0  2  0  3  0 | * 10 *  *
      . β3β3o   ♦ 12 |  0  0  24 12 |  0  8  4  0  0 12 | *  * 5  *
sefa( x3β3β3o ) ♦  6 |  2  1   4  2 |  0  0  0  2  1  2 | *  * * 30

starting figure: x3x3x3o