⭳

Looks like a compound of 2 truncated dodecahedra (tid), and indeed vertices, edges, and {10} all coincide by pairs.

Incidence matrix according to Dynkin symbol

x3/2x5x5*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*a |  10 |  5  0  5 |  * 12  *
.   x5x    |  10 |  0  5  5 |  *  * 12

snubbed forms: s3/2s5s5*a

β3x5x

both( . . . ) | 120 |  1  1  1 |  1  1  1
--------------+-----+----------+---------
both( . x . ) |   2 | 60  *  * |  1  1  0
both( . . x ) |   2 |  * 60  * |  0  1  1
sefa( β3x . ) |   2 |  *  * 60 |  1  0  1
--------------+-----+----------+---------
      β3x .   ♦   6 |  3  0  3 | 20  *  *
both( . x5x ) |  10 |  5  5  0 |  * 12  *
sefa( β3x5x ) |  10 |  0  5  5 |  *  * 12

starting figure: x3x5x