This non-compact hyperbolic tesselation uses the squat in the sense of an infinite horohedron for some of its cells.

This hyperbolic honeycomb is a paracompact member of the general family o4s4oPo, which would be hypercompact from P>4 on.

Incidence matrix according to Dynkin symbol

x4o4o *b3o   (N,M → ∞)

. . .    . | NM ♦  12 |  24 |  6  8
-----------+----+-----+-----+------
x . .    . |  2 | 6NM |   4 |  2  2
-----------+----+-----+-----+------
x4o .    . |  4 |   4 | 6NM |  1  1
-----------+----+-----+-----+------
x4o4o    . ♦  M |  2M |   M | 6N  *
x4o . *b3o ♦  8 |  12 |   6 |  * NM

o3o4o4s   (N,M → ∞)

demi( . . . . ) | NM ♦  12 |  24 |  6  8
----------------+----+-----+-----+------
      . . o4s   |  2 | 6NM |   4 |  2  2
----------------+----+-----+-----+------
sefa( . o4o4s ) |  4 |   4 | 6NM |  1  1
----------------+----+-----+-----+------
      . o4o4s   ♦  M |  2M |   M | 6N  *
sefa( o3o4o4s ) ♦  8 |  12 |   6 |  * NM

starting figure: o3o4o4x

o4s4o4o   (N,M,K → ∞)

demi( . . . . ) | NMK ♦    4    8 |   16    8 |   4   2   8
----------------+-----+-----------+-----------+------------
      o4s . .   |   2 | 2NMK    * |    4    0 |   2   0   2
      . s4o .   |   2 |    * 4NMK |    2    2 |   1   1   2
----------------+-----+-----------+-----------+------------
sefa( o4s4o . ) |   4 |    2    2 | 4NMK    * |   1   0   1
sefa( . s4o4o ) |   4 |    0    4 |    * 2NMK |   0   1   1
----------------+-----+-----------+-----------+------------
      o4s4o .   ♦   M |    M    M |    M    0 | 4NK   *   *
      . s4o4o   ♦   K |    0   2K |    0    K |   * 2NM   *
sefa( o4s4o4o ) ♦   8 |    4    8 |    4    2 |   *   * NMK

starting figure: o4x4o4o

o4s4o *b4o   (N,M,K,L → ∞)

demi( . . .    . ) | NMKL ♦     4     4     4 |     8     8     8 |    2    2    2    8
-------------------+------+-------------------+-------------------+--------------------
      o4s .    .   |    2 | 2NMKL     *     * |     2     2     0 |    1    1    0    2
      . s4o    .   |    2 |     * 2NMKL     * |     2     0     2 |    1    0    1    2
      . s . *b4o   |    2 |     *     * 2NMKL |     0     2     2 |    0    1    1    2
-------------------+------+-------------------+-------------------+--------------------
sefa( o4s4o    . ) |    4 |     2     2     0 | 2NMKL     *     * |    1    0    0    1
sefa( o4s . *b4o ) |    4 |     2     0     2 |     * 2NMKL     * |    0    1    0    1
sefa( . s4o *b4o ) |    4 |     0     2     2 |     *     * 2NMKL |    0    0    1    1
-------------------+------+-------------------+-------------------+--------------------
      o4s4o    .   ♦    M |     M     M     0 |     M     0     0 | 2NKL    *    *    *
      o4s . *b4o   ♦    K |     K     0     K |     0     K     0 |    * 2NML    *    *
      . s4o *b4o   ♦    L |     0     L     L |     0     0     L |    *    * 2NMK    *
sefa( o4s4o *b4o ) ♦    8 |     4     4     4 |     2     2     2 |    *    *    * NMKL

starting figure: o4x4o *b4o

s4o4s *b4o   (N,M,K,L → ∞)

demi( . . .    . ) | NMKL ♦     4     4     4 |    16    4    4 |    4   1   1    8
-------------------+------+-------------------+-----------------+------------------
      s4o .    .   |    2 | 2NMKL     *     * |     2    2    0 |    1   1   0    2
      s 2 s    .   |    2 |     * 2NMKL     * |     4    0    0 |    2   0   0    2
      . o4s    .   |    2 |     *     * 2NMKL |     2    0    2 |    1   0   1    2
-------------------+------+-------------------+-----------------+------------------
sefa( s4o4s    . ) |    4 |     1     2     1 | 4NMKL    *    * |    1   0   0    1
sefa( s4o . *b4o ) |    4 |     4     0     0 |     * NMKL    * |    0   1   0    1
sefa( . o4s *b4o ) |    4 |     0     0     4 |     *    * NMKL |    0   0   1    1
-------------------+------+-------------------+-----------------+------------------
      s4o4s    .   ♦   2M |     M    2M     M |    2M    0    0 | 2NKL   *   *    *
      s4o . *b4o   ♦    K |    2K     0     0 |     0    K    0 |    * NML   *    *
      . o4s *b4o   ♦    L |     0     0    2L |     0    0    L |    *   * NMK    *
sefa( s4o4s *b4o ) ♦    8 |     4     4     4 |     4    1    1 |    *   *   * NMKL

starting figure: x4o4x *b4o

s4o4s4o4*a   (N,M,K,L,P → ∞)

demi( . . . .    ) | NMKLP ♦     2      4     2     2     2 |      8     4      8     4 |    2    1    2    1     8
-------------------+-------+--------------------------------+---------------------------+--------------------------
      s4o . .      |     2 | NMKLP      *     *     *     * |      2     2      0     0 |    1    1    0    0     2
      s 2 s .      |     2 |     * 2NMKLP     *     *     * |      2     0      2     0 |    1    0    1    0     2
      s . . o4*a   |     2 |     *      * NMKLP     *     * |      0     2      2     0 |    0    1    1    0     2
      . o4s .      |     2 |     *      *     * NMKLP     * |      2     0      0     2 |    1    0    0    1     2
      . . s4o      |     2 |     *      *     *     * NMKLP |      0     0      2     2 |    0    0    1    1     2
-------------------+-------+--------------------------------+---------------------------+--------------------------
sefa( s4o4s .    ) |     4 |     1      2     0     1     0 | 2NMKLP     *      *     * |    1    0    0    0     1
sefa( s4o . o4*a ) |     4 |     2      0     2     0     0 |      * NMKLP      *     * |    0    1    0    0     1
sefa( s . s4o4*a ) |     4 |     0      2     1     0     1 |      *     * 2NMKLP     * |    0    0    1    0     1
sefa( . o4s4o    ) |     4 |     0      0     0     2     2 |      *     *      * NMKLP |    0    0    0    1     1
-------------------+-------+--------------------------------+---------------------------+--------------------------
      s4o4s .      ♦    2M |     M     2M     0     M     0 |     2M     0      0     0 | NKLP    *    *    *     *
      s4o . o4*a   ♦     K |     K      0     K     0     0 |      0     K      0     0 |    * NMLP    *    *     *
      s . s4o4*a   ♦    2L |     0     2L     L     0     L |      0     0     2L     0 |    *    * NMKP    *     *
      . o4s4o      ♦     P |     0      0     0     P     P |      0     0      0     P |    *    *    * NMKL     *
sefa( s4o4s4o4*a ) ♦     8 |     2      4     2     2     2 |      2     1      2     1 |    *    *    *    * NMKLP

starting figure: x4o4x4o4*a