This para-compact hyperbolic tesselation uses the sadit in the sense of an infinite horoteron as one of its facet types.

Incidence matrix according to Dynkin symbol

o3o3o3o4s3s   (N,M → ∞)

demi( . . . . . . ) | 48NM ♦    10    10 |    5    30    30 |    10   10    20    40 |    5  10    5    25 |   1   5    6
--------------------+------+-------------+------------------+------------------------+---------------------+-------------
      . . . o4s .   |    2 | 240NM     * |    0     6     2 |     3    1     6     6 |    3   3    2     6 |   1   3    2
sefa( . . . . s3s ) |    2 |     * 240NM |    1     0     4 |     0    4     0     6 |    0   6    0     4 |   0   4    1
--------------------+------+-------------+------------------+------------------------+---------------------+-------------
      . . . . s3s   |    3 |     0     3 | 80NM     *     * |     0    4     0     0 |    0   6    0     0 |   0   4    0
sefa( . . o3o4s . ) |    3 |     3     0 |    * 480NM     * |     1    0     2     1 |    2   1    1     2 |   1   2    1
sefa( . . . o4s3s ) |    3 |     1     2 |    *     * 480NM |     0    1     0     3 |    0   3    0     3 |   0   3    1
--------------------+------+-------------+------------------+------------------------+---------------------+-------------
      . . o3o4s .   ♦    4 |     6     0 |    0     4     0 | 120NM    *     *     * |    2   1    0     0 |   1   2    0
      . . . o4s3s   ♦   12 |     6    24 |    8     0    12 |     * 40NM     *     * |    0   3    0     0 |   0   3    0
sefa( . o3o3o4s . ) ♦    4 |     6     0 |    0     4     0 |     *    * 240NM     * |    1   0    1     1 |   1   1    1
sefa( . . o3o4s3s ) ♦    4 |     3     3 |    0     1     3 |     *    *     * 480NM |    0   1    0     2 |   0   2    1
--------------------+------+-------------+------------------+------------------------+---------------------+-------------
      . o3o3o4s .   ♦    8 |    24     0 |    0    32     0 |     8    0     8     0 | 30NM   *    *     * |   1   1    0
      . . o3o4s3s   ♦   96 |   144   288 |   96    96   288 |    24   24     0    96 |    * 5NM    *     * |   0   2    0
sefa( o3o3o3o4s . ) ♦    5 |    10     0 |    0    10     0 |     0    0     5     0 |    *   * 48NM     * |   1   0    1
sefa( . o3o3o4s3s ) ♦    5 |     6     4 |    0     4     6 |     0    0     1     4 |    *   *    * 240NM |   0   1    1
--------------------+------+-------------+------------------+------------------------+---------------------+-------------
      o3o3o3o4s .   ♦   16 |    80     0 |    0   160     0 |    40    0    80     0 |   10   0   16     0 | 3NM   *    *
      . o3o3o4s3s   ♦  24M |   72M   96M |  32M   96M  144M |   24M  12M   24M   96M |   3M   M    0   24M |   * 10N    *
sefa( o3o3o3o4s3s ) ♦    6 |    10     5 |    0    10    10 |     0    0     5    10 |    0   0    1     5 |   *   * 48NM

starting figure: o3o3o3o4x3x