Looks like a compound of 4 octahedra (oct), and indeed in type A vertices, edges coincide by 4, while {6/2} coincide by pairs, whereas in type B edges coincide by 4, vertices coincide by pairs, and triangles coincide by pairs with one {6/2} each.

Incidence matrix according to Dynkin symbol

x3/2x3β3*a   (type A)

both( .   . .    ) | 24 |  1  1  1  1 | 1 1 1 1
-------------------+----+-------------+--------
both( x   . .    ) |  2 | 12  *  *  * | 1 1 0 0
both( .   x .    ) |  2 |  * 12  *  * | 1 0 1 0
sefa( x   . β3*a ) |  2 |  *  * 12  * | 0 1 0 1
sefa( .   x3β    ) |  2 |  *  *  * 12 | 0 0 1 1
-------------------+----+-------------+--------
both( x3/2x .    ) |  6 |  3  3  0  0 | 4 * * *
      x   . β3*a   ♦  6 |  3  0  3  0 | * 4 * *
      .   x3β      ♦  6 |  0  3  0  3 | * * 4 *
sefa( x3/2x3β3*a ) |  6 |  0  0  3  3 | * * * 4

or
both( .   . .    )    | 24 |  2  2 | 1 2 1
----------------------+----+-------+------
both( x   . .    )  & |  2 | 24  * | 1 1 0
sefa( x   . β3*a )  & |  2 |  * 24 | 0 1 1
----------------------+----+-------+------
both( x3/2x .    )    |  6 |  6  0 | 4 * *
      x   . β3*a    & ♦  6 |  3  3 | * 8 *
sefa( x3/2x3β3*a )    |  6 |  0  6 | * * 4

starting figure: x3/2x3x3*a

β3/2x3β3*a   (type B)

demi( .   . .    ) | 12 |  2  4  2 | 1 2 2  3
-------------------+----+----------+---------
both( .   x .    ) |  2 | 12  *  * | 1 0 1  0
sefa( s   . s3*a ) |  2 |  * 24  * | 0 1 0  1
sefa( .   x3β    ) |  2 |  *  * 12 | 0 0 1  1
-------------------+----+----------+---------
      β3/2x .      ♦  3 |  3  0  0 | 4 * *  *
both( s   . s3*a ) ♦  3 |  0  3  0 | * 8 *  *
      .   x3β      ♦  6 |  3  0  3 | * * 4  *
sefa( β3/2x3β3*a ) |  3 |  0  2  1 | * * * 12

starting figure: x3/2x3x3*a