Looks like a compound of 3 icosahedra (ike) and a great dodecahedron (gad), and indeed vertices coincide by five, edges coincide by four, {3} and {6/2} coincide.

Incidence matrix according to Dynkin symbol

x3/2x3o5*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  *
.   x3o    |  3 |  0  3 |  *  * 20

x5/4o3/2x3/2*a

.   .   .      | 60 |  2  2 |  1  2  1
---------------+----+-------+---------
x   .   .      |  2 | 60  * |  1  1  0
.   .   x      |  2 |  * 60 |  0  1  1
---------------+----+-------+---------
x5/4o   .      |  5 |  5  0 | 12  *  *
x   .   x3/2*a |  6 |  3  3 |  * 20  *
.   o3/2x      |  3 |  0  3 |  *  * 20