Looks like a compound of 2 truncated tetrahedra (tut), and indeed edges, and hexagonal faces all coincide by pairs.

Incidence matrix according to Dynkin symbol

x3/2x3x3*a 

.   . .    | 24 |  1  1  1 | 1 1 1
-----------+----+----------+------
x   . .    |  2 | 12  *  * | 1 1 0
.   x .    |  2 |  * 12  * | 1 0 1
.   . x    |  2 |  *  * 12 | 0 1 1
-----------+----+----------+------
x3/2x .    |  6 |  3  3  0 | 4 * *
x   . x3*a |  6 |  3  0  3 | * 4 *
.   x3x    |  6 |  0  3  3 | * * 4

snubbed forms: β3/2x3x3*a, x3/2x3β3*a, β3/2β3x3*a, β3/2x3β3*a, s3/2s3s3*a

β3x3x 

both( . . . ) | 24 |  1  1  1 | 1 1 1
--------------+----+----------+------
both( . x . ) |  2 | 12  *  * | 1 1 0
both( . . x ) |  2 |  * 12  * | 0 1 1
sefa( β3x . ) |  2 |  *  * 12 | 1 0 1
--------------+----+----------+------
      β3x .   ♦  6 |  3  0  3 | 4 * *
both( . x3x ) |  6 |  3  3  0 | * 4 *
sefa( β3x3x ) |  6 |  0  3  3 | * * 4

starting figure: x3x3x