This non-compact hyperbolic tesselation uses the euclidean tiling that in the sense of an infinite horohedron as cell.

It can be derived as partial Stott contraction of x4o3x3x3*b, when that one will use a 3-coloring of hips, contracting the lacing heights of one (e.g. the g ones below).

A further contraction results then in pex-o4o3x3x3*b.

Incidence matrix

pac-x4o3x3x3*b   (N,M → ∞)
(|g|→0, i.e.: |gy|→0 & |gb|→0)

6NM   *    * |   1    2    4   0    0   0   0 |   1   2    4    4   0    0   0 |   2   2   0  2  ry
  * 6NM    * |   0    2    0   1    4   0   0 |   1   0    0    4   2    4   0 |   2   0   2  2  rb
  *   * 12NM |   0    0    2   0    2   1   1 |   0   1    2    2   1    2   1 |   2   1   1  1  yb
-------------+--------------------------------+--------------------------------+---------------
  2   0    0 | 3NM    *    *   *    *   *   * |   0   0    4    0   0    0   0 |   2   2   0  0  vr
  1   1    0 |   * 12NM    *   *    *   *   * |   1   0    0    2   0    0   0 |   1   0   0  2  r
  1   0    1 |   *    * 24NM   *    *   *   * |   0   1    1    1   0    0   0 |   1   1   0  1  y
  0   2    0 |   *    *    * 3NM    *   *   * |   0   0    0    0   0    4   0 |   2   0   2  0  or
  0   1    1 |   *    *    *   * 24NM   *   * |   0   0    0    1   1    1   0 |   1   0   1  1  b
  0   0    2 |   *    *    *   *    * 6NM   * |   0   0    2    0   0    0   1 |   2   1   0  0  vb
  0   0    2 |   *    *    *   *    *   * 6NM |   0   0    0    0   0    2   1 |   2   0   1  0  oy
-------------+--------------------------------+--------------------------------+---------------
  3   3    0 |   0    6    0   0    0   0   0 | 2NM   *    *    *   *    *   * |   0   0   0  2  r
  3   0    3 |   0    0    6   0    0   0   0 |   * 4NM    *    *   *    *   * |   0   1   0  1  y
  2   0    2 |   1    0    2   0    0   1   0 |   *   * 12NM    *   *    *   * |   1   1   0  0  vr-y-vb-y
  1   1    1 |   0    1    1   0    1   0   0 |   *   *    * 24NM   *    *   * |   1   0   0  1  ryb
  0   3    3 |   0    0    0   0    6   0   0 |   *   *    *    * 4NM    *   * |   0   0   1  1  b
  0   2    2 |   0    0    0   1    2   0   1 |   *   *    *    *   * 12NM   * |   1   0   1  0  or-b-oy-b
  0   0    4 |   0    0    0   0    0   2   2 |   *   *    *    *   *    * 3NM |   2   0   0  0  vb-oy-vb-oy
-------------+--------------------------------+--------------------------------+---------------
  4   4    8 |   2    4    8   2    8   4   4 |   0   0    4    8   0    4   2 | 3NM   *   *  *  squobcu
  6   0    6 |   3    0   12   0    0   3   0 |   0   2    6    0   0    0   0 |   * 2NM   *  *  y-hip
  0   6    6 |   0    0    0   3   12   0   3 |   0   0    0    0   2    6   0 |   *   * 2NM  *  b-hip
 3M  3M   3M |   0   6M   6M   0   6M   0   0 |   M   M    0   6M   M    0   0 |   *   *   * 4N  that