This non-compact hyperbolic tesselation uses squats and tosquats in the sense of an infinite horohedron is its cells.

Incidence matrix according to Dynkin symbol

x4x4o4o   (N,M,K → ∞)

. . . . | 2NMK |   1    4 |   4    4 |   4   1
--------+------+----------+----------+--------
x . . . |    2 | NMK    * |   4    0 |   4   0
. x . . |    2 |   * 4NMK |   1    2 |   2   1
--------+------+----------+----------+--------
x4x . . |    8 |   4    4 | NMK    * |   2   0
. x4o . |    4 |   0    4 |   * 2NMK |   1   1
--------+------+----------+----------+--------
x4x4o . ♦   4M |  2M   4M |   M    M | 2NK   *
. x4o4o ♦    K |   0   2K |   0    K |   * 2NM

x4x4o *b4o   (N,M,K,L → ∞)

. . .    . | 2NMKL |    1     4 |    4    2    2 |   2   2   1
-----------+-------+------------+----------------+------------
x . .    . |     2 | NMKL     * |    4    0    0 |   2   2   0
. x .    . |     2 |    * 4NMKL |    1    1    1 |   1   1   1
-----------+-------+------------+----------------+------------
x4x .    . |     8 |    4     4 | NMKL    *    * |   1   1   0
. x4o    . |     4 |    0     4 |    * NMKL    * |   1   0   1
. x . *b4o |     4 |    0     4 |    *    * NMKL |   0   1   1
-----------+-------+------------+----------------+------------
x4x4o    . ♦    4M |   2M    4M |    M    M    0 | NKL   *   *
x4x . *b4o ♦    4K |   2K    4K |    K    0    K |   * NML   *
. x4o *b4o ♦    2L |    0    4L |    0    L    L |   *   * NMK

x4xØx4*a4xØx4*a   (N,M,K,L,P,Q → ∞)

. . .    . .    | 8NMKLPQ |       1       1       1       1       1 |      1      1      1      1       1       1       1       1 |     1     1     1     1      1
----------------+---------+-----------------------------------------+-------------------------------------------------------------+-------------------------------
x . .    . .    |       2 | 4NMKLPQ       *       *       *       * |      1      1      1      1       0       0       0       0 |     1     1     1     1      0
. x .    . .    |       2 |       * 4NMKLPQ       *       *       * |      1      0      0      0       1       1       0       0 |     1     1     0     0      1
. . x    . .    |       2 |       *       * 4NMKLPQ       *       * |      0      1      0      0       0       0       1       1 |     0     0     1     1      1
. . .    x .    |       2 |       *       *       * 4NMKLPQ       * |      0      0      1      0       1       0       1       0 |     1     0     1     0      1
. . .    . x    |       2 |       *       *       *       * 4NMKLPQ |      0      0      0      1       0       1       0       1 |     0     1     0     1      1
----------------+---------+-----------------------------------------+-------------------------------------------------------------+-------------------------------
x4x .    . .    |       8 |       4       4       0       0       0 | NMKLPQ      *      *      *       *       *       *       * |     1     1     0     0      0
x . x4*a . .    |       8 |       4       0       4       0       0 |      * NMKLPQ      *      *       *       *       *       * |     0     0     1     1      0
x . . *a4x .    |       8 |       4       0       0       4       0 |      *      * NMKLPQ      *       *       *       *       * |     1     0     1     0      0
x . .    . x4*a |       8 |       4       0       0       0       4 |      *      *      * NMKLPQ       *       *       *       * |     0     1     0     1      0
. x .    x .    |       4 |       0       2       0       2       0 |      *      *      *      * 2NMKLPQ       *       *       * |     1     0     0     0      1
. x .    . x    |       4 |       0       2       0       0       2 |      *      *      *      *       * 2NMKLPQ       *       * |     0     1     0     0      1
. . x    x .    |       4 |       0       0       2       2       0 |      *      *      *      *       *       * 2NMKLPQ       * |     0     0     1     0      1
. . x    . x    |       4 |       0       0       2       0       2 |      *      *      *      *       *       *       * 2NMKLPQ |     0     0     0     1      1
----------------+---------+-----------------------------------------+-------------------------------------------------------------+-------------------------------
x4x . *a4x .    ♦      8M |      4M      4M       0      4M       0 |      M      0      M      0      2M       0       0       0 | NKLPQ     *     *     *      *
x4x .    . x4*a ♦      8K |      4K      4K       0       0      4K |      K      0      0      K       0      2K       0       0 |     * NMLPQ     *     *      *
x . x4*a4x .    ♦      8L |      4L       0      4L      4L       0 |      0      L      L      0       0       0      2L       0 |     *     * NMKPQ     *      *
x . x4*a . x4*a ♦      8P |      4P       0      4P       0      4P |      0      P      0      P       0       0       0      2P |     *     *     * NMKLQ      *
. xØx    xØx    ♦      4Q |       0      2Q      2Q      2Q      2Q |      0      0      0      0       Q       Q       Q       Q |     *     *     *     * 2NMKLP