This non-compact hyperbolic tesselation uses the euclidean tiling squat in the sense of an infinite horohedron as its single cell type.

The vertex figure should be a variant of the tetragonal partial Stott expaded co, i.e. of uxu4oqo&#xt.

Incidence matrix according to Dynkin symbol

o4xØx4*a4xØo4*a

. . .    . .    | NMKLPQ |       4       4       8 |      4      4      4       8       8 |     4     1     4     1      4
----------------+--------+-------------------------+--------------------------------------+-------------------------------
. x .    . .    |      2 | 2NMKLPQ       *       * |      2      0      0       2       0 |     2     1     0     0      1
. . x    . .    |      2 |       * 2NMKLPQ       * |      0      2      0       0       2 |     0     0     2     1      1
. . .    x .    |      2 |       *       * 4NMKLPQ |      0      0      1       1       1 |     1     0     1     0      1
----------------+--------+-------------------------+--------------------------------------+-------------------------------
o4x .    . .    |      4 |       4       0       0 | NMKLPQ      *      *       *       * |     1     1     0     0      0
o . x4*a . .    |      4 |       0       4       0 |      * NMKLPQ      *       *       * |     0     0     1     1      0
o . . *a4x .    |      4 |       0       0       4 |      *      * NMKLPQ       *       * |     1     0     1     0      0
. x .    x .    |      4 |       2       0       2 |      *      *      * 2NMKLPQ       * |     1     0     0     0      1
. . x    x .    |      4 |       0       2       2 |      *      *      *       * 2NMKLPQ |     0     0     1     0      1
----------------+--------+-------------------------+--------------------------------------+-------------------------------
o4x . *a4x .    ♦     4M |      4M       0      4M |      M      0      M      2M       0 | NKLPQ     *     *     *      *
o4x .    . o4*a ♦      K |      2K       0       0 |      K      0      0       0       0 |     * NMLPQ     *     *      *
o . x4*a4x .    ♦     4L |       0      4L      4L |      0      L      L       0      2K |     *     * NMKPQ     *      *
o . x4*a . o4*a ♦      P |       0      2P       0 |      0      P      0       0       0 |     *     *     * NMKLQ      *
. xØx    xØo    ♦     2Q |       Q       Q      2Q |      0      0      0       Q       Q |     *     *     *     * 2NMKLP

octahedral Coxeter domain with boundary pattern:

  b    e
g    a  
        
  h    c
d    f  

oØxØxØxØoØxØxØxØ*aØ*cØ*gØ*eØ*hØ*fØ*bØ*dØ*a   (N,M,K,L,P,Q,R → ∞)
a b c d e f g h

. . . . . . . .                            | NMKLPQR |       2       2        4       2       2        4 |       4       4       4       4       4       4       4 |      1      1      2      2      4      4
-------------------------------------------+---------+---------------------------------------------------+---------------------------------------------------------+------------------------------------------
. x . . . . . .                            |       2 | NMKLPQR       *        *       *       *        * |       2       2       0       0       0       0       0 |      1      0      0      1      2      0
. . x . . . . .                            |       2 |       * NMKLPQR        *       *       *        * |       0       0       2       2       0       0       0 |      0      1      0      1      0      2
. . . x . . . .                            |       2 |       *       * 2NMKLPQR       *       *        * |       0       0       0       0       1       1       1 |      0      0      1      0      1      1
. . . . . x . .                            |       2 |       *       *        * NMKLPQR       *        * |       0       0       2       0       2       0       0 |      0      1      1      0      0      2
. . . . . . x .                            |       2 |       *       *        *       * NMKLPQR        * |       2       0       0       0       0       2       0 |      1      0      1      0      2      0
. . . . . . . x                            |       2 |       *       *        *       *       * 2NMKLPQR |       0       1       0       1       0       0       1 |      0      0      0      1      1      1
-------------------------------------------+---------+---------------------------------------------------+---------------------------------------------------------+------------------------------------------
. x . . . . x .                            |       4 |       2       0        0       0       2        0 | NMKLPQR       *       *       *       *       *       * |      1      0      0      0      1      0
. x . . . . . x                            |       4 |       2       0        0       0       0        2 |       * NMKLPQR       *       *       *       *       * |      0      0      0      1      1      0
. . x . . x . .                            |       4 |       0       2        0       2       0        0 |       *       * NMKLPQR       *       *       *       * |      0      1      0      0      0      1
. . x . . . . x                            |       4 |       0       2        0       0       0        2 |       *       *       * NMKLPQR       *       *       * |      0      0      0      1      0      1
. . . x . x . .                            |       4 |       0       0        2       2       0        0 |       *       *       *       * NMKLPQR       *       * |      0      0      1      0      0      1
. . . x . . x .                            |       4 |       0       0        2       0       2        0 |       *       *       *       *       * NMKLPQR       * |      0      0      1      0      1      0
. . . x . . . x                            |       4 |       0       0        2       0       0        2 |       *       *       *       *       *       * NMKLPQR |      0      0      0      0      1      1
-------------------------------------------+---------+---------------------------------------------------+---------------------------------------------------------+------------------------------------------
oØx . . o . x .       *gØ*e                ♦       M |       M       0        0       0       M        0 |       M       0       0       0       0       0       0 | NKLPQR      *      *      *      *      *
o . x . oØx . . *aØ*c                      ♦       K |       0       K        0       K       0        0 |       0       0       K       0       0       0       0 |      * NMLPQR      *      *      *      *
o . . x . xØx .                      *dØ*a ♦      2L |       0       0       2L       L       L        0 |       0       0       0       0       L       L       0 |      *      * NMKPQR      *      *      *
. xØx . o . . x          *eØ*h             ♦      2P |       P       P        0       0       0       2P |       0       P       0       P       0       0       0 |      *      *      * NMKLQR      *      *
. x . x . . xØx                   *bØ*d    ♦      4Q |      2Q       0       2Q       0      2Q       2Q |       Q       Q       0       0       0       Q       Q |      *      *      *      * NMKLPR      *
. . xØx . x . x             *hØ*f          ♦      4R |       0      2R       2R      2R       0       2R |       0       0       R       R       R       0       R |      *      *      *      *      * NMKLPQ

or
NMKL |     8     8 |     8    16    4 |    2    4    8
-----+-------------+------------------+---------------
   2 | 4NMKL     * |     2     2    0 |    1    1    2  b,c,f,g
   2 |     * 4NMKL |     0     2    1 |    0    1    2  d,h
-----+-------------+------------------+---------------
   4 |     4     0 | 2NMKL     *    * |    1    0    1
   4 |     2     2 |     * 4NMKL    * |    0    1    1
   4 |     0     4 |     *     * NMKL |    0    0    2
-----+-------------+------------------+---------------
♦  M |    2M     0 |     M     0    0 | 2NKL    *    *
♦  K |     K     K |     0     K    0 |    * 4NML    *
♦ 4L |    4L    4L |     L    2L    L |    *    * 2NMK