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

Incidence matrix according to Dynkin symbol

x5/4x3x5*a

.   . .    | 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   . x5*a |  10 |  5  0  5 |  * 12  *
.   x3x    |   6 |  0  3  3 |  *  * 20