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

Incidence matrix according to Dynkin symbol

x5/4x3o5*a

.   . .    | 60 |  2  2 |  2  1  1
-----------+----+-------+---------
x   . .    |  2 | 60  * |  1  1  0
.   x .    |  2 |  * 60 |  1  0  1
-----------+----+-------+---------
x5/4x .    | 10 |  5  5 | 12  *  *
x   . o5*a |  5 |  5  0 |  * 12  *
.   x3o    |  3 |  0  3 |  *  * 20

x5/4x5/4o3/2*a

.   .   .      | 60 |  2  2 |  2  1  1
---------------+----+-------+---------
x   .   .      |  2 | 60  * |  1  1  0
.   x   .      |  2 |  * 60 |  1  0  1
---------------+----+-------+---------
x5/4x   .      | 10 |  5  5 | 12  *  *
x   .   o3/2*a |  3 |  3  0 |  * 20  *
.   x5/4o      |  5 |  0  5 |  *  * 12