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Looks like acompound 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 toDynkin symbol

β3β3oboth( . . .    ) |12 |  2  2  2 | 1 1 1  3-----------------+----+----------+---------sefa( s3s . (r)) |  2 | 12  *  * | 1 0 0  1sefa( s3s . (l)) |  2 |  * 12  * | 0 1 0  1sefa( . 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

orboth( . . . ) |12 |  4  2 | 2 1  3--------------+----+-------+-------sefa( s3s . ) |  2 | 24  * | 1 0  1sefa( . β3o ) |  2 |  * 12 | 0 1  1--------------+----+-------+-------both( s3s . )♦  3 |  3  0 | 8 *  *      . β3o♦  3 |  0  3 | * 4  *sefa( β3β3o ) |  3 |  2  1 | * * 12starting figure:x3x3o

s3/2s3s3*ademi( .   . .    ) |12 |  2  2  2 | 1 1 1  3-------------------+----+----------+---------sefa( s3/2s .    ) |  2 | 12  *  * | 1 0 0  1sefa( s   . s3*a ) |  2 |  * 12  * | 0 1 0  1sefa( .   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

ordemi( .   . .    )    |12 |  2  4 | 1 2  3----------------------+----+-------+-------sefa( s3/2s .    )    |  2 | 12  * | 1 0  1sefa( 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 | * * 12starting figure:x3/2x3x3*a

o3/2β3βboth( .   . . ) |12 |  2  4 | 1 2  3----------------+----+-------+-------sefa( o3/2β . ) |  2 | 12  * | 1 0  1sefa( .   s3s ) |  2 |  * 24 | 0 1  1----------------+----+-------+-------      o3/2β .♦  3 |  3  0 | 4 *  *both( .   s3s )♦  3 |  0  3 | * 8  *sefa( o3/2β3β ) |  3 |  1  2 | * * 12starting figure:o3/2x3x