This regular non-compact hyperbolic tesselation uses the tetrahedral-octahedral honeycomb in the sense of an infinite horochoron as one of its cells.

Incidence matrix according to Dynkin symbol

s3s4o3o4o   (N,M → ∞)

demi( . . . . . ) | 12NM ♦   12   12 |    6    36   24 |   12    8   32    6 |  8   1    7
------------------+------+-----------+-----------------+---------------------+------------
      . s4o . .   |    2 | 72NM    * |    0     2    4 |    1    2    4    2 |  2   1    2
sefa( s3s . . . ) |    2 |    * 72NM |    1     4    0 |    4    0    4    0 |  4   0    1
------------------+------+-----------+-----------------+---------------------+------------
      s3s . . .   |    3 |    0    3 | 24NM     *    * |    4    0    0    0 |  4   0    0
sefa( s3s4o . . ) |    3 |    1    2 |    * 144NM    * |    1    0    2    0 |  2   0    1
sefa( . s4o3o . ) |    3 |    3    0 |    *     * 96NM |    0    1    1    1 |  1   1    1
------------------+------+-----------+-----------------+---------------------+------------
      s3s4o . .   ♦   12 |    6   24 |    8    12    0 | 12NM    *    *    * |  2   0    0
      . s4o3o .   ♦    4 |    6    0 |    0     0    4 |    * 24NM    *    * |  1   1    0
sefa( s3s4o3o . ) ♦    4 |    3    3 |    0     3    1 |    *    * 96NM    * |  1   0    1
sefa( . s4o3o4o ) ♦    6 |   12    0 |    0     0    8 |    *    *    * 12NM |  0   1    1
------------------+------+-----------+-----------------+---------------------+------------
      s3s4o3o .   ♦   96 |  144  288 |   96   288   96 |   24   24   96    0 | NM   *    *
      . s4o3o4o   ♦    M |   6M    0 |    0     0   8M |    0   2M    0    M |  * 12N    *
sefa( s3s4o3o4o ) ♦    7 |   12    6 |    0    12    8 |    0    0    8    1 |  *   * 12NM

starting figure: x3x4o3o4o