This non-compact hyperbolic tesselation uses squat in the sense of an infinite horohedron as one of its cell types.

Incidence matrix according to Dynkin symbol

o3xØo3*a3xØo3*a   (N,M → ∞)

. . .    . .    | NM ♦  12  12 |  12  12  24 | 12  4  4  6
----------------+----+---------+-------------+------------
. x .    . .    |  2 | 6NM   * |   2   0   2 |  2  1  0  1
. . .    x .    |  2 |   * 6NM |   0   2   2 |  2  0  1  1
----------------+----+---------+-------------+------------
o3x .    . .    |  3 |   3   0 | 4NM   *   * |  1  1  0  0
o . . *a3x .    |  3 |   0   3 |   * 4NM   * |  1  0  1  0
. x .    x .    |  4 |   2   2 |   *   * 6NM |  1  0  0  1
----------------+----+---------+-------------+------------
o3x . *a3x .    ♦ 12 |  12  12 |   4   4   6 | NM  *  *  *
o3x .    . o3*a ♦  4 |   6   0 |   4   0   0 |  * NM  *  *
o . o3*a3x .    ♦  4 |   0   6 |   0   4   0 |  *  * NM  *
. xØo    xØo    ♦  M |   M   M |   0   0   M |  *  *  * 6N

o3o3o4s4*a   (N,M → ∞)

hemi( . . . .    ) | NM ♦  12  12 |  12  24  12 |  4  6  4 12
-------------------+----+---------+-------------+------------
      o . . s4*a   |  2 | 6NM   * |   2   2   0 |  1  1  0  2
      . . o4s      |  2 |   * 6NM |   0   2   2 |  0  1  1  2
-------------------+----+---------+-------------+------------
sefa( o3o . s4*a ) |  3 |   3   0 | 4NM   *   * |  1  0  0  1
sefa( o . o4s4*a ) |  4 |   2   2 |   * 6NM   * |  0  1  0  1
sefa( . o3o4s    ) |  3 |   0   3 |   *   * 4NM |  0  0  1  1
-------------------+----+---------+-------------+------------
      o3o . s4*a   ♦  4 |   6   0 |   4   0   0 | NM  *  *  *
      o . o4s4*a   ♦  M |   M   M |   0   M   0 |  * 6N  *  *
      . o3o4s      ♦  4 |   0   6 |   0   0   4 |  *  * NM  *
sefa( o3o3o4s4*a ) ♦ 12 |  12  12 |   4   6   4 |  *  *  * NM

starting figure: o3o3o4x4*a