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

Incidence matrix according to Dynkin symbol

x4x4o *b3x   (N,M → ∞)

. . .    . | 24NM |    1    2    1 |   2   1   1   2 |  1  2  1
-----------+------+----------------+-----------------+---------
x . .    . |    2 | 12NM    *    * |   2   1   0   0 |  1  2  0
. x .    . |    2 |    * 24NM    * |   1   0   1   1 |  1  1  1
. . .    x |    2 |    *    * 12NM |   0   1   0   2 |  0  2  1
-----------+------+----------------+-----------------+---------
x4x .    . |    8 |    4    4    0 | 6NM   *   *   * |  1  1  0
x . .    x |    4 |    2    0    2 |   * 6NM   *   * |  0  2  0
. x4o    . |    4 |    0    4    0 |   *   * 6NM   * |  1  0  1
. x . *b3x |    6 |    0    3    3 |   *   *   * 8NM |  0  1  1
-----------+------+----------------+-----------------+---------
x4x4o    . ♦   4M |   2M   4M    0 |   M   0   M   0 | 6N  *  *
x4x . *b3x ♦   48 |   24   24   24 |   6  12   0   8 |  * NM  *
. x4o *b3x ♦   24 |    0   24   12 |   0   0   6   8 |  *  * NM

snubbed forms: x4s4o *b3s

x3x4o4s   (N,M → ∞)

demi( . . . . ) | 24NM |    1    2    1 |   2   1   1   2 |  1  1  2
----------------+------+----------------+-----------------+---------
demi( x . . . ) |    2 | 12NM    *    * |   2   0   1   0 |  1  0  2
demi( . x . . ) |    2 |    * 24NM    * |   1   1   0   1 |  1  1  1
          o4s   |    2 |    *    * 12NM |   0   0   1   2 |  0  1  2
----------------+------+----------------+-----------------+---------
demi( x3x . . ) |    6 |    3    3    0 | 8NM   *   *   * |  1  0  1
demi( . x4o . ) |    4 |    0    4    0 |   * 6NM   *   * |  1  1  0
      x 2 o4s   |    4 |    2    0    2 |   *   * 6NM   * |  0  0  2
sefa( . x4o4s ) |    8 |    0    4    4 |   *   *   * 6NM |  0  1  1
----------------+------+----------------+-----------------+---------
demi( x3x4o . ) ♦   24 |   12   24    0 |   8   6   0   0 | NM  *  *
      . x4o4s   ♦   4M |    0   4M   2M |   0   M   0   M |  * 6N  *
sefa( x3x4o4s ) ♦   48 |   24   24   24 |   8   0  12   6 |  *  * NM

starting figure: x3x4o4x