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

o3xØo4*a3oØx4*a   (N,M,K → ∞)

. . .    . .    | NMK |    24    24 |   24   24    48 |    8  24   6   12
----------------+-----+-------------+-----------------+------------------
. x .    . .    |   2 | 12NMK     * |    2    0     2 |    1   2   0    1
. . .    . x    |   2 |     * 12NMK |    0    2     2 |    0   2   1    1
----------------+-----+-------------+-----------------+------------------
o3x .    . .    |   3 |     3     0 | 8NMK    *     * |    1   1   0    0
o . .    . x4*a |   4 |     0     4 |    * 6NMK     * |    0   1   1    0
. x .    . x    |   4 |     2     2 |    *    * 12NMK |    0   1   0    1
----------------+-----+-------------+-----------------+------------------
o3x . *a3o .    ♦   4 |     6     0 |    4    0     0 | 2NMK   *   *    *
o3x .    . x4*a ♦  24 |    24    24 |    8    6    12 |    * NMK   *    *
o . o4*a . x4*a ♦   M |     0    2M |    0    M     0 |    *   * 6NK    *
. xØo    oØx    ♦   K |     K     K |    0    0     K |    *   *   * 12NM

o3o4s4o4*a   (N,M,K → ∞)

hemi( . . . .    ) | NMK |    24    24 |   24   24    48 |    8   6   12  24
-------------------+-----+-------------+-----------------+------------------
      . o4s .      |   2 | 12NMK     * |    2    0     2 |    1   0    1   2
      . . s4o      |   2 |     * 12NMK |    0    2     2 |    0   1    1   2
-------------------+-----+-------------+-----------------+------------------
sefa( o3o4s .    ) |   3 |     3     0 | 8NMK    *     * |    1   0    0   1
sefa( o . s4o4*a ) |   4 |     0     4 |    * 6NMK     * |    0   1    0   1
sefa( . o4s4o    ) |   4 |     2     2 |    *    * 12NMK |    0   0    1   1
-------------------+-----+-------------+-----------------+------------------
      o3o4s .      ♦   4 |     6     0 |    4    0     0 | 2NMK   *    *   *
      o . s4o4*a   ♦   M |     0    2M |    0    M     0 |    * 6NK    *   *
      . o4s4o      ♦   K |     K     K |    0    0     K |    *   * 12NM   *
sefa( o3o4s4o4*a ) ♦  24 |    24    24 |    8    6    12 |    *   *    * NMK

starting figure: o3o4x4o4*a