Looks like a compound of 2 icosahedra (ike) plus 4 great dodecahedra (gad), and indeed vertices coincide by ten, edges coincide by six, {10/2} coincide by pairs.

Incidence matrix according to Dynkin symbol

x3/2x5/2x5/2*a

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