Looks like a compound of a small ditrigonary icosidodecahedron (sidtid) plus a ditrigonary dodecadodecahedron (ditdid) plus a great ditrigonary icosidodecahedron (gidtid), and indeed vertices coincide by 6, edges coincide by three.

Incidence matrix according to Dynkin symbol

x3/2x5/2x

.   .   . | 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  *
.   x5/2x |  10 |  0  5  5 |  *  * 12