This hyperbolic tetracomb implements in a ridge faceting subspace the hyperbolic honeycomb spidded.

Incidence matrix according to Dynkin symbol

x5o3o3o5x   (N → ∞)

. . . . . | 600N |     4     4 |    6    12    6 |    4   12   12    4 | 1   4    6   4 1
----------+------+-------------+-----------------+---------------------+-----------------
x . . . . |    2 | 1200N     * |    3     3    0 |    3    6    3    0 | 1   3    3   1 0
. . . . x |    2 |     * 1200N |    0     3    3 |    0    3    6    3 | 0   1    3   3 1
----------+------+-------------+-----------------+---------------------+-----------------
x5o . . . |    5 |     5     0 | 720N     *    * |    2    2    0    0 | 1   2    1   0 0
x . . . x |    4 |     2     2 |    * 1800N    * |    0    2    2    0 | 0   1    2   1 0
. . . o5x |    5 |     0     5 |    *     * 720N |    0    0    2    2 | 0   0    1   2 1
----------+------+-------------+-----------------+---------------------+-----------------
x5o3o . . ♦   20 |    30     0 |   12     0    0 | 120N    *    *    * | 1   1    0   0 0
x5o . . x ♦   10 |    10     5 |    2     5    0 |    * 720N    *    * | 0   1    1   0 0
x . . o5x ♦   10 |     5    10 |    0     5    2 |    *    * 720N    * | 0   0    1   1 0
. . o3o5x ♦   20 |     0    30 |    0     0   12 |    *    *    * 120N | 0   0    0   1 1
----------+------+-------------+-----------------+---------------------+-----------------
x5o3o3o . ♦  600 |  1200     0 |  720     0    0 |  120    0    0    0 | N   *    *   * *
x5o3o . x ♦   40 |    60    20 |   24    30    0 |    2   12    0    0 | * 60N    *   * *
x5o . o5x ♦   25 |    25    25 |    5    25    5 |    0    5    5    0 | *   * 144N   * *
x . o3o5x ♦   40 |    20    60 |    0    30   24 |    0    0   12    2 | *   *    * 60N *
. o3o3o5x ♦  600 |     0  1200 |    0     0  720 |    0    0    0  120 | *   *    *   * N

or
. . . . .    | 300N |     8 |   12   12 |    8   24 | 2   8   6
-------------+------+-------+-----------+-----------+----------
x . . . .  & |    2 | 1200N |    3    3 |    3    9 | 1   4   3
-------------+------+-------+-----------+-----------+----------
x5o . . .  & |    5 |     5 | 720N    * |    2    2 | 1   2   1
x . . . x    |    4 |     4 |    * 900N |    0    4 | 0   2   2
-------------+------+-------+-----------+-----------+----------
x5o3o . .  & ♦   20 |    30 |   12    0 | 120N    * | 1   1   0
x5o . . x  & ♦   10 |    15 |    2    5 |    * 720N | 0   1   1
-------------+------+-------+-----------+-----------+----------
x5o3o3o .  & ♦  600 |  1200 |  720    0 |  120    0 | N   *   *
x5o3o . x  & ♦   40 |    80 |   24   30 |    2   12 | * 60N   *
x5o . o5x    ♦   25 |    50 |   10   25 |    0   10 | *   * 72N