This non-compact hyperbolic tesselation uses squat in the sense of an infinite horohedron for some of its cells.

Incidence matrix according to Dynkin symbol

o3o4x4o4*a   (N,M,K → ∞)

. . . .    | NMK ♦    24 |   24   24 |   8   6  12
-----------+-----+-------+-----------+------------
. . x .    |   2 | 12NMK |    2    2 |   1   1   2
-----------+-----+-------+-----------+------------
. o4x .    |   4 |     4 | 6NMK    * |   1   0   1
. . x4o    |   4 |     4 |    * 6NMK |   0   1   1
-----------+-----+-------+-----------+------------
o3o4x .    ♦   8 |    12 |    6    0 | NMK   *   *
o . x4o4*a ♦   M |    2M |    0    M |   * 6NK   *
. o4x4o    ♦  2K |    4K |    K    K |   *   * 6NM

snubbed forms: o3o4s4o4*a

o3oØx4*a3oØx4*a   (N,M,K → ∞)

. . .    . .    | 2NMK ♦    12    12 |   12   12    24 |   4   4  12    6
----------------+------+-------------+-----------------+-----------------
. . x    . .    |    2 | 12NMK     * |    2    0     2 |   0   1   2    1
. . .    . x    |    2 |     * 12NMK |    0    2     2 |   1   0   2    1
----------------+------+-------------+-----------------+-----------------
o . x4*a . .    |    4 |     4     0 | 6NMK    *     * |   0   1   1    0
o . .    . x4*a |    4 |     0     4 |    * 6NMK     * |   1   0   1    0
. . x    . x    |    4 |     2     2 |    *    * 12NMK |   0   0   1    1
----------------+------+-------------+-----------------+-----------------
o3o .    . x4*a ♦    8 |     0    12 |    0    6     0 | NMK   *   *    *
o . x4*a3o .    ♦    8 |    12     0 |    6    0     0 |   * NMK   *    *
o . x4*a . x4*a ♦   4M |    4M    4M |    M    M    2M |   *   * 6NK    *
. oØx    oØx    ♦    K |     K     K |    0    0     K |   *   *   * 12NM