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

Incidence matrix according to Dynkin symbol

x3/2x5/2o5*a

.   .   .    | 60 |  2  2 |  2  1  1
-------------+----+-------+---------
x   .   .    |  2 | 60  * |  1  1  0
.   x   .    |  2 |  * 60 |  1  0  1
-------------+----+-------+---------
x3/2x   .    |  6 |  3  3 | 20  *  *
x   .   o5*a |  5 |  5  0 |  * 12  *
.   x5/2o    |  5 |  0  5 |  *  * 12

o5/4x3/2x5/3*a

.   .   .      | 60 |  2  2 |  1  2  1
---------------+----+-------+---------
.   x   .      |  2 | 60  * |  1  1  0
.   .   x      |  2 |  * 60 |  0  1  1
---------------+----+-------+---------
o5/4x   .      |  5 |  5  0 | 12  *  *
.   x3/2x      |  6 |  3  3 |  * 20  *
o    .  x5/3*a |  5 |  0  5 |  *  * 12