Looks like a compound of 6 dodecahedra (doe), and indeed vertices and edges both coincide by six, {10/2} coincide by three.

Incidence matrix according to Dynkin symbol

x5/2x5/2x5/2*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
---------------+-----+----------+---------
x5/2x   .      |  10 |  5  5  0 | 12  *  *
x   .   x5/2*a |  10 |  5  0  5 |  * 12  *
.   x5/2x      |  10 |  0  5  5 |  *  * 12

snubbed forms: s5/2s5/2s5/2*a

x5/2x5β

both( .   . . ) | 120 |  1  1  1 |  1  1  1
----------------+-----+----------+---------
both( x   . . ) |   2 | 60  *  * |  1  0  1
both( .   x . ) |   2 |  * 60  * |  1  1  0
sefa( .   x5β ) |   2 |  *  * 60 |  0  1  1
----------------+-----+----------+---------
both( x5/2x . ) |  10 |  5  5  0 | 12  *  *
      .   x5β   ♦  10 |  0  5  5 |  * 12  *
sefa( x5/2x5β ) |  10 |  5  0  5 |  *  * 12

starting figure: x5/2x5x