Looks like a compound of a cubohemioctahedron (cho) plus 4 {6/2} fitting into one of the tetrahedral sets of holes, and indeed the vertices and {6/2}-edges both coincide by pairs.

Incidence matrix according to Dynkin symbol

x3/2x3x

.   . . | 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   . x |  4 |  2  0  2 | * 6 *
.   x3x |  6 |  0  3  3 | * * 4

snubbed forms: β3/2x3x, x3/2β3x, x3/2x3β, β3/2β3x, β3/2x3β