Looks like a compound of 2 truncated icosahedra (ti), and indeed the vertices, edges, and {6} all coincide by pairs.

Incidence matrix according to Dynkin symbol

x5/2x3x3*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   . x3*a |   6 |  3  0  3 |  * 20  *
.   x3x    |   6 |  0  3  3 |  *  * 20

snubbed forms: s5/2s3s3*a

β5x3x

both( . . . ) | 120 |  1  1  1 |  1  1  1
--------------+-----+----------+---------
both( . x . ) |   2 | 60  *  * |  1  1  0
both( . . x ) |   2 |  * 60  * |  0  1  1
sefa( β5x . ) |   2 |  *  * 60 |  1  0  1
--------------+-----+----------+---------
      β5x .   ♦  10 |  5  0  5 | 12  *  *
both( . x3x ) |   6 |  3  3  0 |  * 20  *
sefa( β5x3x ) |   6 |  0  3  3 |  *  * 20

starting figure: x5x3x