This hypercompact hyperbolic tesselation uses thisquat in the sense of an infinite bollohedron as one of its cell types.

Incidence matrix according to Dynkin symbol

o3x3x4x4*b   (N,M → ∞)

. . . .    | 24NM |    2    1    1 |   1   2   2   1 |   1  1  2
-----------+------+----------------+-----------------+----------
. x . .    |    2 | 24NM    *    * |   1   1   1   0 |   1  1  1
. . x .    |    2 |    * 12NM    * |   0   2   0   1 |   1  0  2
. . . x    |    2 |    *    * 12NM |   0   0   2   1 |   0  1  2
-----------+------+----------------+-----------------+----------
o3x . .    |    3 |    3    0    0 | 8NM   *   *   * |   1  1  0
. x3x .    |    6 |    3    3    0 |   * 8NM   *   * |   1  0  1
. x . x4*b |    8 |    4    0    4 |   *   * 6NM   * |   0  1  1
. . x4x    |    8 |    0    4    4 |   *   *   * 3NM |   0  0  2
-----------+------+----------------+-----------------+----------
o3x3x .    ♦   12 |   12    6    0 |   4   4   0   0 | 2NM  *  *
o3x . x4*b ♦   24 |   24    0   12 |   8   0   6   0 |   * NM  *
. x3x4x4*b ♦  24M |  12M  12M  12M |   0  4M  3M  3M |   *  * 2N

trunc( o3o3o4x4*b )   (N,M → ∞)

trops( . . . x    ) | 24NM |    1    2    1 |   2   1   1   2 |  1  2   1
--------------------+------+----------------+-----------------+----------
trunc( . . . x    ) |    2 | 12NM    *    * |   2   1   0   0 |  1  2   0
verf(  . o . x4*b ) |    2 |    * 24NM    * |   1   0   1   1 |  1  1   1
verf(  . . o4x    ) |    2 |    *    * 12NM |   0   1   0   2 |  0  2   1
--------------------+------+----------------+-----------------+----------
trunc( . o . x4*b ) |    8 |    4    4    0 | 6NM   *   *   * |  1  1   0
trunc( . . o4x    ) |    8 |    4    0    4 |   * 3NM   *   * |  0  2   0
verf(  o3o . x4*b ) |    3 |    0    3    0 |   *   * 8NM   * |  1  0   1
verf(  . o3o4x4*b ) |    6 |    0    3    3 |   *   *   * 8NM |  0  1   1
--------------------+------+----------------+-----------------+----------
trunc( o3o . x4*b ) ♦   24 |   12   24    0 |   6   0   8   0 | NM  *   *
trunc( . o3o4x4*b ) ♦  24M |  12M  12M  12M |  3M  3M   0  4M |  * 2N   *
verf(  o3o3o4x4*b ) ♦   12 |    0   12    6 |   0   0   4   4 |  *  * 2NM