Looks like a compound of 2 octahedra plus 4 pairs of coincident triangles arranged tetrahedrally. And indeed in tetrahedral positions retrograd triangles {3/2} are coincident with 3 more prograde ones, whereas the opposite tetrahedral positions are taken by pairs of {3}. Vertices coincide by pairs and edges coincide by three.

Incidence matrix according to Dynkin symbol

β3β3o

both( . . .    ) | 12 |  2  2  2 | 1 1 1  3
-----------------+----+----------+---------
sefa( s3s . (r)) |  2 | 12  *  * | 1 0 0  1
sefa( s3s . (l)) |  2 |  * 12  * | 0 1 0  1
sefa( . β3o    ) |  2 |  *  * 12 | 0 0 1  1
-----------------+----+----------+---------
      s3s . (r)  ♦  3 |  3  0  0 | 4 * *  *
      s3s . (l)  ♦  3 |  0  3  0 | * 4 *  *
      . β3o      ♦  3 |  0  0  3 | * * 4  *
sefa( β3β3o    ) |  3 |  1  1  1 | * * * 12

or
both( . . . ) | 12 |  4  2 | 2 1  3
--------------+----+-------+-------
sefa( s3s . ) |  2 | 24  * | 1 0  1
sefa( . β3o ) |  2 |  * 12 | 0 1  1
--------------+----+-------+-------
both( s3s . ) ♦  3 |  3  0 | 8 *  *
      . β3o   ♦  3 |  0  3 | * 4  *
sefa( β3β3o ) |  3 |  2  1 | * * 12

starting figure: x3x3o

s3/2s3s3*a

demi( .   . .    ) | 12 |  2  2  2 | 1 1 1  3
-------------------+----+----------+---------
sefa( s3/2s .    ) |  2 | 12  *  * | 1 0 0  1
sefa( s   . s3*a ) |  2 |  * 12  * | 0 1 0  1
sefa( .   s3s    ) |  2 |  *  * 12 | 0 0 1  1
-------------------+----+----------+---------
      s3/2s .      ♦  3 |  3  0  0 | 4 * *  *
      s   . s3*a   ♦  3 |  0  3  0 | * 4 *  *
      .   s3s      ♦  3 |  0  0  3 | * * 4  *
sefa( s3/2s3s3*a ) |  3 |  1  1  1 | * * * 12

or
demi( .   . .    )    | 12 |  2  4 | 1 2  3
----------------------+----+-------+-------
sefa( s3/2s .    )    |  2 | 12  * | 1 0  1
sefa( s   . s3*a )  & |  2 |  * 24 | 0 1  1
----------------------+----+-------+-------
      s3/2s .         ♦  3 |  3  0 | 4 *  *
      s   . s3*a    & ♦  3 |  0  3 | * 8  *
sefa( s3/2s3s3*a    ) |  3 |  1  2 | * * 12

starting figure: x3/2x3x3*a

o3/2β3β

both( .   . . ) | 12 |  2  4 | 1 2  3
----------------+----+-------+-------
sefa( o3/2β . ) |  2 | 12  * | 1 0  1
sefa( .   s3s ) |  2 |  * 24 | 0 1  1
----------------+----+-------+-------
      o3/2β .   ♦  3 |  3  0 | 4 *  *
both( .   s3s ) ♦  3 |  0  3 | * 8  *
sefa( o3/2β3β ) |  3 |  1  2 | * * 12

starting figure: o3/2x3x