This noble non-compact hyperbolic tesselation uses toxat in the sense of an infinite horohedron as its only cell type.

Incidence matrix according to Dynkin symbol

o3x6x3o   (N,M,K → ∞)

. . . . | 3NMK |    2    2 |   1   4   1 |  2  2
--------+------+-----------+-------------+------
. x . . |    2 | 3NMK    * |   1   2   0 |  2  1
. . x . |    2 |    * 3NMK |   0   2   1 |  1  2
--------+------+-----------+-------------+------
o3x . . |    3 |    3    0 | NMK   *   * |  2  0
. x6x . |   12 |    6    6 |   * NMK   * |  1  1
. . x3o |    3 |    0    3 |   *   * NMK |  0  2
--------+------+-----------+-------------+------
o3x6x . ♦   6M |   6M   3M |  2M   M   0 | NK  *
. x6x3o ♦   6K |   3K   6K |   0   K  2K |  * NM

or
. . . .    | 3NM |   4 |   2  4 |  4
-----------+-----+-----+--------+---
. x . .  & |   2 | 6NM |   1  2 |  3
-----------+-----+-----+--------+---
o3x . .  & |   3 |   3 | 2NM  * |  2
. x6x .    |  12 |  12 |   * NM |  2
-----------+-----+-----+--------+---
o3x6x .  & ♦  6M |  9M |  2M  M | 2N