Looks like a compound of 2 rectified pentachora (rap) plus 20 additional tetrahedra (tet) in pentachoral positions coincident by 4 each.

Incidence matrix according to Dynkin symbol

β3β3o3o

both( . . . . ) | 20 |  6  6 |  3  3  9  3 | 3 1  4
----------------+----+-------+-------------+-------
sefa( s3s . . ) |  2 | 60  * |  1  0  2  0 | 2 0  1
sefa( . β3o . ) |  2 |  * 60 |  0  1  1  1 | 1 1  1
----------------+----+-------+-------------+-------
both( s3s . . ) ♦  3 |  3  0 | 20  *  *  * | 2 0  0
      . β3o .   ♦  3 |  0  3 |  * 20  *  * | 1 1  0
sefa( β3β3o . ) |  3 |  2  1 |  *  * 60  * | 1 0  1
sefa( . β3o3o ) |  3 |  0  3 |  *  *  * 20 | 0 1  1
----------------+----+-------+-------------+-------
      β3β3o .   ♦ 12 | 24 12 |  8  4 12  0 | 5 *  *
      . β3o3o   ♦  4 |  0 12 |  0  4  0  4 | * 5  *
sefa( β3β3o3o ) ♦  4 |  3  3 |  0  0  3  1 | * * 20

starting figure: x3x3o3o