Looks like a compound of 2 small dodecahemidodecahedron (sidtid) plus rhom, the compound of 5 cubes (cube), and indeed vertices coincide by 6, edges coincide by three.

Incidence matrix according to Dynkin symbol

x5/4x3/2x

.   .   . | 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
----------+-----+----------+---------
x5/4x   . |  10 |  5  5  0 | 12  *  *
x   .   x |   4 |  2  0  2 |  * 30  *
.   x3/2x |   6 |  0  3  3 |  *  * 20