This non-compact hyperbolic tesselation uses both the euclidean tilings hexat and rothat in the sense of infinite horohedra as some of its cells.

Incidence matrix according to Dynkin symbol

x3o3o *b6x   (N,M,K → ∞)

. . .    . | 4NMK |    3    3 |    3    3    3 |   1   3   1
-----------+------+-----------+----------------+------------
x . .    . |    2 | 6NMK    * |    2    1    0 |   1   2   0
. . .    x |    2 |    * 6NMK |    0    1    2 |   0   2   1
-----------+------+-----------+----------------+------------
x3o .    . |    3 |    3    0 | 4NMK    *    * |   1   1   0
x . .    x |    4 |    2    2 |    * 3NMK    * |   0   2   0
. o . *b6x |    6 |    0    6 |    *    * 2NMK |   0   1   1
-----------+------+-----------+----------------+------------
x3o3o    . ♦    4 |    6    0 |    4    0    0 | NMK   *   *
x3o . *b6x ♦   6M |   6M   6M |   2M   3M    M |   * 2NK   *
. o3o *b6x ♦   2K |    0   3K |    0    0    K |   *   * 2NM

snubbed forms: x3o3o *b6s

s4o3o6x   (N,M,K → ∞)

demi( . . . . ) | 4NMK |    3    3 |    3    3    3 |   1   1   3
----------------+------+-----------+----------------+------------
demi( . . . x ) |    2 | 6NMK    * |    2    1    0 |   1   0   2
      s4o . .   |    2 |    * 6NMK |    0    1    2 |   0   1   2
----------------+------+-----------+----------------+------------
demi( . . o6x ) |    6 |    6    0 | 2NMK    *    * |   1   0   1
      s4o 2 x   |    4 |    2    2 |    * 3NMK    * |   0   0   2
sefa( s4o3o . ) |    3 |    0    3 |    *    * 4NMK |   0   1   1
----------------+------+-----------+----------------+------------
demi( . o3o6x ) ♦   2M |   3M    0 |    M    0    0 | 2NK   *   *
      s4o3o .   ♦    4 |    0    6 |    0    0    4 |   * NMK   *
sefa( s4o3o6x ) ♦   6K |   6K   6K |    K   3K   2K |   *   * 2NM

starting figure: x4o3o6x