Acronym ...
Name hyperbolic honeycomb with seed point at face of right-angled octahedron domain

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 here is kind a threefold axial version of (the axially forefold) rad with three rhombs connected to the poles each and further three rhombs around its equator. (Its edge skeleton would be a representation of the Herschel graph.)


Incidence matrix according to Dynkin symbol

octahedral Coxeter domain with boundary pattern:

  b    e
g    a  
        
  h    c
d    f  

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

. . . . . . . .                            | 2NMKLPQR |        2        2        2       1       1       1        2 |       2       2       2       2       2       2       2       2       2 |      1      1      1      2      2      2
-------------------------------------------+----------+-------------------------------------------------------------+-------------------------------------------------------------------------+------------------------------------------
. x . . . . . .                            |        2 | 2NMKLPQR        *        *       *       *       *        * |       1       1       1       0       0       0       0       0       0 |      1      0      0      1      1      0
. . x . . . . .                            |        2 |        * 2NMKLPQR        *       *       *       *        * |       0       0       0       1       1       1       0       0       0 |      0      1      0      1      0      1
. . . x . . . .                            |        2 |        *        * 2NMKLPQR       *       *       *        * |       0       0       0       0       0       0       1       1       1 |      0      0      1      0      1      1
. . . . x . . .                            |        2 |        *        *        * NMKLPQR       *       *        * |       2       0       0       2       0       0       0       0       0 |      1      1      0      2      0      0
. . . . . x . .                            |        2 |        *        *        *       * NMKLPQR       *        * |       0       0       0       0       2       0       2       0       0 |      0      1      1      0      0      2
. . . . . . x .                            |        2 |        *        *        *       *       * NMKLPQR        * |       0       2       0       0       0       0       0       2       0 |      1      0      1      0      2      0
. . . . . . . x                            |        2 |        *        *        *       *       *       * 2NMKLPQR |       0       0       1       0       0       1       0       0       1 |      0      0      0      1      1      1
-------------------------------------------+----------+-------------------------------------------------------------+-------------------------------------------------------------------------+------------------------------------------
. x . . x . . .                            |        4 |        2        0        0       2       0       0        0 | NMKLPQR       *       *       *       *       *       *       *       * |      1      0      0      1      0      0
. x . . . . x .                            |        4 |        2        0        0       0       0       2        0 |       * NMKLPQR       *       *       *       *       *       *       * |      1      0      0      0      1      0
. x . . . . . x                            |        4 |        2        0        0       0       0       0        2 |       *       * NMKLPQR       *       *       *       *       *       * |      0      0      0      1      1      0
. . x . x . . .                            |        4 |        0        2        0       2       0       0        0 |       *       *       * NMKLPQR       *       *       *       *       * |      0      1      0      1      0      0
. . x . . x . .                            |        4 |        0        2        0       0       2       0        0 |       *       *       *       * NMKLPQR       *       *       *       * |      0      1      0      0      0      1
. . x . . . . x                            |        4 |        0        2        0       0       0       0        2 |       *       *       *       *       * NMKLPQR       *       *       * |      0      0      0      1      0      1
. . . x . x . .                            |        4 |        0        0        2       0       2       0        0 |       *       *       *       *       *       * NMKLPQR       *       * |      0      0      1      0      0      1
. . . x . . x .                            |        4 |        0        0        2       0       0       2        0 |       *       *       *       *       *       *       * NMKLPQR       * |      0      0      1      0      1      0
. . . x . . . x                            |        4 |        0        0        2       0       0       0        2 |       *       *       *       *       *       *       *       * NMKLPQR |      0      0      0      0      1      1
-------------------------------------------+----------+-------------------------------------------------------------+-------------------------------------------------------------------------+------------------------------------------
oØx . . x . x .       *gØ*e                       2M |       2M        0        0       M       0       M        0 |       M       M       0       0       0       0       0       0       0 | NKLPQR      *      *      *      *      *
o . x . xØx . . *aØ*c                             2K |        0       2K        0       K       K       0        0 |       0       0       0       K       K       0       0       0       0 |      * NMLPQR      *      *      *      *
o . . x . xØx .                      *dØ*a        2L |        0        0       2L       0       L       L        0 |       0       0       0       0       0       0       L       L       0 |      *      * NMKPQR      *      *      *
. xØx . x . . x          *eØ*h                    4P |       2P       2P        0      2P       0       0       2P |       P       0       P       P       0       P       0       0       0 |      *      *      * NMKLQR      *      *
. x . x . . xØx                   *bØ*d           4Q |       2Q        0       2Q       0       0      2Q       2Q |       0       Q       Q       0       0       0       0       Q       Q |      *      *      *      * NMKLPR      *
. . xØx . x . x             *hØ*f                 4R |        0       2R       2R       0      2R       0       2R |       0       0       0       0       R       R       R       0       R |      *      *      *      *      * NMKLPQ
or
2NMK |    2    6    3 |    6   12 |   6   3
-----+----------------+-----------+--------
   2 | 2NMK    *    * |    3    0 |   3   0
   2 |    * 6NMK    * |    1    2 |   2   1
   2 |    *    * 3NMK |    0    4 |   2   2
-----+----------------+-----------+--------
   4 |    2    2    0 | 3NMK    * |   2   0
   4 |    0    2    2 |    * 6NMK |   1   1
-----+----------------+-----------+--------
 2M |    M   2M    M |    M    M | 6NK   *
  K |    0    K    K |    0    K |   * 6NM

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