Looks like a compound of 2 great dodecahemidodecahedron (gidhid), and indeed vertices, edges, and faces all coincide by pairs

Incidence matrix according to Dynkin symbol

x5/3x5/3o5/2*a

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