Looks like a compound of 2 truncated cubes (tic), and indeed vertices, edges, and {8} all coincide by pairs.

Incidence matrix according to Dynkin symbol

x3/2x4x4*a

.   . .    | 48 |  1  1  1 | 1 1 1
-----------+----+----------+------
x   . .    |  2 | 24  *  * | 1 1 0
.   x .    |  2 |  * 24  * | 1 0 1
.   . x    |  2 |  *  * 24 | 0 1 1
-----------+----+----------+------
x3/2x .    |  6 |  3  3  0 | 8 * *
x   . x4*a |  8 |  4  0  4 | * 6 *
.   x4x    |  8 |  0  4  4 | * * 6

β3x4x

both( . . . ) | 48 |  1  1  1 | 1 1 1
--------------+----+----------+------
both( . x . ) |  2 | 24  *  * | 1 1 0
both( . . x ) |  2 |  * 24  * | 0 1 1
sefa( β3x . ) |  2 |  *  * 24 | 1 0 1
--------------+----+----------+------
      β3x .   ♦  6 |  3  0  3 | 8 * *
both( . x4x ) |  8 |  4  4  0 | * 6 *
sefa( β3x4x ) |  8 |  0  4  4 | * * 6

starting figure: x3x4x