Looks like a compound of 4 tetrahedra (tet) with vertices identified, edges coincide by four, and each {6/2} coincides with 2 triangles.

Incidence matrix according to Dynkin symbol

β3/2o3o3*a

both( .   . .    ) | 4 |  6  6 | 3 3 6
-------------------+---+-------+------
sefa( β3/2o .    ) | 2 | 12  * | 1 0 1
sefa( β   . o3*a ) | 2 |  * 12 | 0 1 1
-------------------+---+-------+------
      β3/2o .      ♦ 3 |  3  0 | 4 * *
      β   . o3*a   ♦ 3 |  0  3 | * 4 *
sefa( β3/2o3o3*a ) | 6 |  3  3 | * * 4

starting figure: x3/2o3o3*a

o3/2o3β3*a

both( .   . .    ) | 4 |  6  6 | 3 3 6
-------------------+---+-------+------
sefa( .   o3β    ) | 2 | 12  * | 1 0 1
sefa( o   . β3*a ) | 2 |  * 12 | 0 1 1
-------------------+---+-------+------
      .   o3β      ♦ 3 |  3  0 | 4 * *
      o   . β3*a   ♦ 3 |  0  3 | * 4 *
sefa( o3/2o3β3*a ) | 6 |  3  3 | * * 4

or
both( .   . .    )    | 4 | 12 | 6 6
----------------------+---+----+----
sefa( .   o3β    )  & | 2 | 24 | 1 1
----------------------+---+----+----
      .   o3β       & ♦ 3 |  3 | 8 *
sefa( o3/2o3β3*a )    | 6 |  6 | * 4

starting figure: o3/2o3x3*a

β3/2o3/2o3/2*a

both( .   .   .      ) | 4 |  6  6 | 3 3 6
-----------------------+---+-------+------
sefa( β3/2o   .      ) | 2 | 12  * | 1 0 1
sefa( β   .   o3/2*a ) | 2 |  * 12 | 0 1 1
-----------------------+---+-------+------
      β3/2o   .        ♦ 3 |  3  0 | 4 * *
      β   .   o3/2*a   ♦ 3 |  0  3 | * 4 *
sefa( β3/2o3/2o3/2*a ) | 6 |  3  3 | * * 4

or
both( .   .   .      )    | 4 | 12 | 6 6
--------------------------+---+----+----
sefa( β3/2o   .      )  & | 2 | 24 | 1 1
--------------------------+---+----+----
      β3/2o   .         & ♦ 3 |  3 | 8 *
sefa( β3/2o3/2o3/2*a )    | 6 |  6 | * 4

starting figure: x3/2o3/2o3/2*a