Looks like a compound of small rhombidodecahedron (sird) plus 20 {6/2} fitting into the icosahedral set of holes, and indeed vertices and {6/2}-edges both coincide by pairs.

Incidence matrix according to Dynkin symbol

x3/2x5x

.   . . | 120 |  1  1  1 |  1  1  1
--------+-----+----------+---------
x   . . |   2 | 60  *  * |  1  1  0
.   x . |   2 |  * 60  * |  1  0  1
.   . x |   2 |  *  * 60 |  0  1  1
--------+-----+----------+---------
x3/2x . |   6 |  3  3  0 | 20  *  *
x   . x |   4 |  2  0  2 |  * 30  *
.   x5x |  10 |  0  5  5 |  *  * 12

snubbed forms: s3/2s5s