This non-compact hyperbolic tesselation uses the euclidean tiling hexat in the sense of an infinite horohedron as one of its cells.

Incidence matrix according to Dynkin symbol

x4o3o6x   (N,M → ∞)

. . . . | 8NM |    3    3 |   3    6   3 |  1   3   3  1
--------+-----+-----------+--------------+--------------
x . . . |   2 | 12NM    * |   2    2   0 |  1   2   1  0
. . . x |   2 |    * 12NM |   0    2   2 |  0   1   2  1
--------+-----+-----------+--------------+--------------
x4o . . |   4 |    4    0 | 6NM    *   * |  1   1   0  0
x . . x |   4 |    2    2 |   * 12NM   * |  0   1   1  0
. . o6x |   6 |    0    6 |   *    * 4NM |  0   0   1  1
--------+-----+-----------+--------------+--------------
x4o3o . ♦   8 |   12    0 |   6    0   0 | NM   *   *  *
x4o . x ♦   8 |    8    4 |   2    4   0 |  * 3NM   *  *
x . o6x ♦  12 |    6   12 |   0    6   2 |  *   * 2NM  *
. o3o6x ♦  2M |    0   3M |   0    0   M |  *   *   * 4N

snubbed forms: s4o3o6x, x4o3o6s