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

Incidence matrix according to Dynkin symbol

x3x4o3o4o   (N,M → ∞)

. . . . . | 24NM |    1    6 |    6   12 |   12    8 |  8   1
----------+------+-----------+-----------+-----------+-------
x . . . . |    2 | 12NM    * ♦    6    0 |   12    0 |  8   0
. x . . . |    2 |    * 72NM |    1    4 |    4    4 |  4   1
----------+------+-----------+-----------+-----------+-------
x3x . . . |    6 |    3    3 | 24NM    * |    4    0 |  4   0
. x4o . . |    4 |    0    4 |    * 72NM |    1    2 |  2   1
----------+------+-----------+-----------+-----------+-------
x3x4o . . ♦   24 |   12   24 |    8    6 | 12NM    * |  2   0
. x4o3o . ♦    8 |    0   12 |    0    6 |    * 24NM |  1   1
----------+------+-----------+-----------+-----------+-------
x3x4o3o . ♦  192 |   96  288 |   96  144 |   24   24 | NM   *
. x4o3o4o ♦    M |    0   3M |    0   3M |    0    M |  * 24N

snubbed forms: s3s4o3o4o