Looks like a compound of 6 tetrahedra (tet), and indeed in type A vertices and edges both coincide by six, {6/2} coincide by three. In type B edges coincide by 6, vertices by 3, and pairs of {3} coincide with pairs of {6/2} each. In type C edges and {3} coincide by 6, vertices by 3. In type D vertices coincide by 3, edges by 6, and 4 triangles each coincide with one {6/2}.

Incidence matrix according to Dynkin symbol

x3/2x3/2x3/2*a   (type A)

.   .   .      | 24 |  1  1  1 | 1 1 1
---------------+----+----------+------
x   .   .      |  2 | 12  *  * | 1 1 0
.   x   .      |  2 |  * 12  * | 1 0 1
.   .   x      |  2 |  *  * 12 | 0 1 1
---------------+----+----------+------
x3/2x   .      |  6 |  3  3  0 | 4 * *
x   .   x3/2*a |  6 |  3  0  3 | * 4 *
.   x3/2x      |  6 |  0  3  3 | * * 4

x3/2o3β3*a   (type B)

both( .   . .    ) | 12 |  2  2  2 | 1 2 1 2
-------------------+----+----------+--------
both( x   . .    ) |  2 | 12  *  * | 1 1 0 0
sefa( x   . β3*a ) |  2 |  * 12  * | 0 1 0 1
sefa( .   o3β    ) |  2 |  *  * 12 | 0 0 1 1
-------------------+----+----------+--------
both( x3/2o .    ) |  3 |  3  0  0 | 4 * * *
      x   . β3*a   ♦  6 |  3  3  0 | * 4 * *
      .   o3β      ♦  3 |  0  0  3 | * * 4 *
sefa( x3/2o3β3*a ) |  6 |  0  3  3 | * * * 4

starting figure: x3/2o3x3*a

β3/2β3o   (type C)

both( .   . . ) | 12 |  4  2 | 2 1  3
----------------+----+-------+-------
sefa( s3/2s . ) |  2 | 24  * | 1 0  1
sefa( .   β3o ) |  2 |  * 12 | 0 1  1
----------------+----+-------+-------
both( s3/2s . ) ♦  3 |  3  0 | 8 *  *
      .   β3o   ♦  3 |  0  3 | * 4  *
sefa( β3/2β3o ) |  3 |  2  1 | * * 12

starting figure: x3/2x3o

x3/2x3β   (type A)

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

starting figure: x3/2x3x

β3/2x3β   (type D)

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

starting figure: x3/2x3x