Looks like a compound of 2 coincident tesseractihexadecachora (tah).

Incidence matrix according to Dynkin symbol

β3x3x4o

both( . . . . ) | 192 |  1   2  1 |  2  1  1  2 | 1  2 1
----------------+-----+-----------+-------------+-------
both( . x . . ) |   2 | 96   *  * |  2  0  1  0 | 1  2 0
both( . . x . ) |   2 |  * 192  * |  1  1  0  1 | 1  1 1
sefa( β3x . . ) |   2 |  *   * 96 |  0  0  1  2 | 0  2 1
----------------+-----+-----------+-------------+-------
both( . x3x . ) |   6 |  3   3  0 | 64  *  *  * | 1  1 0
both( . . x4o ) |   4 |  0   4  0 |  * 48  *  * | 1  0 1
      β3x . .   ♦   6 |  3   0  3 |  *  * 32  * | 0  2 0
sefa( β3x3x . ) |   6 |  0   3  3 |  *  *  * 64 | 0  1 1
----------------+-----+-----------+-------------+-------
both( . x3x4o ) ♦  24 | 12  24  0 |  8  6  0  0 | 8  * *
      β3x3x .   ♦  24 | 12  12 12 |  4  0  4  4 | * 16 *
sefa( β3x3x4o ) ♦  24 |  0  24 12 |  0  6  0  8 | *  * 8

starting figure: x3x3x4o

β3x3x *b3x

both( . . .    . ) | 192 |  1  1  1  1 |  1  1  1  1  1  1 | 1 1 1 1
-------------------+-----+-------------+-------------------+--------
both( . x .    . ) |   2 | 96  *  *  * |  1  1  0  1  0  0 | 1 1 1 0
both( . . x    . ) |   2 |  * 96  *  * |  1  0  1  0  1  0 | 1 1 0 1
both( . . .    x ) |   2 |  *  * 96  * |  0  1  1  0  0  1 | 1 0 1 1
sefa( β3x .    . ) |   2 |  *  *  * 96 |  0  0  0  1  1  1 | 0 1 1 1
-------------------+-----+-------------+-------------------+--------
both( . x3x    . ) |   6 |  3  3  0  0 | 32  *  *  *  *  * | 1 1 0 0
both( . x . *b3x ) |   6 |  3  0  3  0 |  * 32  *  *  *  * | 1 0 1 0
both( . . x    x ) |   4 |  0  2  2  0 |  *  * 48  *  *  * | 1 0 0 1
      β3x .    .   ♦   6 |  3  0  0  3 |  *  *  * 32  *  * | 0 1 1 0
sefa( β3x3x    . ) |   6 |  0  3  0  3 |  *  *  *  * 32  * | 0 1 0 1
sefa( β3x . *b3x ) |   6 |  0  0  3  3 |  *  *  *  *  * 32 | 0 0 1 1
-------------------+-----+-------------+-------------------+--------
both( . x3x *b3x ) ♦  24 | 12 12 12  0 |  4  4  6  0  0  0 | 8 * * *
      β3x3x    .   ♦  24 | 12 12  0 12 |  4  0  0  4  4  0 | * 8 * *
      β3x . *b3x   ♦  24 | 12  0 12 12 |  0  4  0  4  0  4 | * * 8 *
sefa( β3x3x *b3x ) ♦  24 |  0 12 12 12 |  0  0  6  0  4  4 | * * * 8

starting figure: x3x3xb3x