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

Incidence matrix according to Dynkin symbol

o5/3x5/2x3*a

.   .   .    | 60 |  2  2 |  1  2  1
-------------+----+-------+---------
.   x   .    |  2 | 60  * |  1  1  0
.   .   x    |  2 |  * 60 |  0  1  1
-------------+----+-------+---------
o5/3x   .    |  5 |  5  0 | 12  *  *
.   x5/2x    | 10 |  5  5 |  * 12  *
o   .   x3*a |  3 |  0  3 |  *  * 20

x3/2o5/2x5/2*a

.   .   .      | 60 |  2  2 |  1  2  1
---------------+----+-------+---------
x   .   .      |  2 | 60  * |  1  1  0
.   .   x      |  2 |  * 60 |  0  1  1
---------------+----+-------+---------
x3/2o   .      |  3 |  3  0 | 20  *  *
x   .   x5/2*a | 10 |  5  5 |  * 12  *
.   o5/2x      |  5 |  0  5 |  *  * 12