Looks like a compound of 2 great icosihemidodecahedron (geihid), and indeed vertices, edges, and faces all coincide by pairs.

Incidence matrix according to Dynkin symbol

o3/2x5/3x3*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   .   o3*a |  3 |  3  0 |  * 20  *
.   x5/3o    |  5 |  0  5 |  *  * 12