Looks like a compound of 3 pentachora (pen) with vertices identified, edges and faces coincide by 3, cells by pairs. One of the coincident cells each is a Grünbaumian double cover of the tetrahedron (2tet (?)) itself.

Incidence matrix according to Dynkin symbol

β3o3o3o

both( . . . . ) | 5 ♦ 12 |  6 12 | 4 4
----------------+---+----+-------+----
sefa( β3o . . ) | 2 | 30 |  1  2 | 2 1
----------------+---+----+-------+----
      β3o . .   ♦ 3 |  3 | 10  * | 2 0
sefa( β3o3o . ) | 3 |  3 |  * 20 | 1 1
----------------+---+----+-------+----
      β3o3o .   ♦ 4 | 12 |  4  4 | 5 *
sefa( β3o3o3o ) ♦ 4 |  6 |  0  4 | * 5