This non-compact hyperbolic tesselation uses trat in the sense of an infinite horohedron as some of its cell types.

Incidence matrix according to Dynkin symbol

x3o6o3x   (N,M,K → ∞)

. . . . | NMK |    6    6 |    6   12    6 |  1   6   6  1
--------+-----+-----------+----------------+--------------
x . . . |   2 | 3NMK    * |    2    2    0 |  1   2   1  0
. . . x |   2 |    * 3NMK |    0    2    2 |  0   1   2  1
--------+-----+-----------+----------------+--------------
x3o . . |   3 |    3    0 | 2NMK    *    * |  1   1   0  0
x . . x |   4 |    2    2 |    * 3NMK    * |  0   1   1  0
. . o3x |   3 |    0    3 |    *    * 2NMK |  0   0   1  1
--------+-----+-----------+----------------+--------------
x3o6o . ♦   M |   3M    0 |   2M    0    0 | NK   *   *  *
x3o . x ♦   6 |    6    3 |    2    3    0 |  * NMK   *  *
x . o3x ♦   6 |    3    6 |    0    3    2 |  *   * NMK  *
. o6o3x ♦   K |    0   3K |    0    0   2K |  *   *   * NM

or
. . . .    | NM |  12 |  12  12 |  2  12
-----------+----+-----+---------+-------
x . . .  & |  2 | 6NM |   2   2 |  1   3
-----------+----+-----+---------+-------
x3o . .  & |  3 |   3 | 4NM   * |  1   1
x . . x    |  4 |   4 |   * 3NM |  0   2
-----------+----+-----+---------+-------
x3o6o .  & ♦  M |  3M |  2M   0 | 2N   *
x3o . x  & ♦  6 |   9 |   2   3 |  * 2NM