Looks like a compound of a rhombicosahedron (ri) plus 12 {10/4} fitting into the dodecahedral set of pentagrammic holes, and indeed vertices and {10/4}-edges both coincide by pairs.

Incidence matrix according to Dynkin symbol

x5/4x3x

.   . . | 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
--------+-----+----------+---------
x5/4x . |  10 |  5  5  0 | 12  *  *
x   . x |   4 |  2  0  2 |  * 30  *
.   x3x |   6 |  0  3  3 |  *  * 20