Looks like a compound of 2 coincident rectified pentachora (rap), and indeed vertices, edges, triangles and tetrahedra (tet) all coincide by pairs.

Incidence matrix according to Dynkin symbol

β3x3o3o

both( . . . . ) | 20 ♦  3  3 |  3  3  3 | 1 3 1
----------------+----+-------+----------+------
both( . x . . ) |  2 | 30  * |  2  1  0 | 1 2 0
sefa( β3x . . ) |  2 |  * 30 |  0  1  2 | 0 2 1
----------------+----+-------+----------+------
both( . x3o . ) |  3 |  3  0 | 20  *  * | 1 1 0
      β3x . .   ♦  6 |  3  3 |  * 10  * | 0 2 0
sefa( β3x3o . ) |  3 |  0  3 |  *  * 20 | 0 1 1
----------------+----+-------+----------+------
both( . x3o3o ) ♦  4 |  6  0 |  4  0  0 | 5 * *
      β3x3o .   ♦ 12 | 12 12 |  4  4  4 | * 5 *
sefa( β3x3o3o ) ♦  4 |  0  6 |  0  0  4 | * * 5

starting figure: x3x3o3o