This non-compact hyperbolic tesselation uses squat in the sense of an infinite horohedron as one of its cell types. Its vertex figure also is a squat variant, in fact x4o4q. (In the representation by o3xØo4*a3xØo4*a its x4o squares would be alternatedly colored, just as in the honeycomb itself the oct then are alternatedly colored.)

Incidence matrix according to Dynkin symbol

x3o3o4o4*a   (N,M → ∞)

. . . .    | 6NK |    4M |   4M   4M |   M  2M   M
-----------+-----+-------+-----------+------------
x . . .    |   2 | 12NMK |    2    2 |   1   2   1
-----------+-----+-------+-----------+------------
x3o . .    |   3 |     3 | 8NMK    * |   1   1   0
x . . o4*a |   4 |     4 |    * 6NMK |   0   1   1
-----------+-----+-------+-----------+------------
x3o4o .    ♦   6 |    12 |    8    0 | NMK   *   *
x3o . o4*a ♦  12 |    24 |    8    6 |   * NMK   *
x . o4o4*a ♦   K |    2K |    0    K |   *   * 6NM

o3xØo4*a3xØo4*a   (N,M,K → ∞)

. . .    . .    | 6NK |    4M    4M |   4M   4M    8M |   4M   M   M   2M
----------------+-----+-------------+-----------------+------------------
. x .    . .    |   2 | 12NMK     * |    2    0     2 |    2   1   0    1
. . .    x .    |   2 |     * 12NMK |    0    2     2 |    2   0   1    1
----------------+-----+-------------+-----------------+------------------
o3x .    . .    |   3 |     3     0 | 8NMK    *     * |    1   1   0    0
o . . *a3x .    |   3 |     0     3 |    * 8NMK     * |    1   0   1    0
. x .    x .    |   4 |     2     2 |    *    * 12NMK |    1   0   0    1
----------------+-----+-------------+-----------------+------------------
o3x . *a3x .    ♦  12 |    12    12 |    4    4     6 | 2NMK   *   *    *
o3x .    . o4*a ♦   6 |    12     0 |    8    0     0 |    * NMK   *    *
o . o4*a3x .    ♦   6 |     0    12 |    0    8     0 |    *   * NMK    *
. xØo    xØo    ♦   K |     K     K |    0    0     K |    *   *   * 12NM