By virtue of an outer symmetry this is a non-quasiregular monotoxal hexacomb, that is all edges belong to the same equivalence class.

Incidence matrix according to Dynkin symbol

x3o3o3o3x *c3o3x   (N → ∞)

. . . . .    . .    | 90N |    24 |    72    96 |    96   288    96 |   48   192   72   288 |  24   3   48   96  144 | 3  24  24
--------------------+-----+-------+-------------+-------------------+-----------------------+------------------------+----------
x . . . .    . .  & |   2 | 1080N |     6     8 |    12    36    12 |    8    32   12    48 |   8   1   10   20   32 | 2   9   6
--------------------+-----+-------+-------------+-------------------+-----------------------+------------------------+----------
x3o . . .    . .  & |   3 |     3 | 2160N     * |     4     4     0 |    4     8    2     4 |   4   1    4    4    4 | 2   4   1
x . . . x    . .  & |   4 |     4 |     * 2160N |     0    12     3 |    0     6    3    15 |   3   0    2    7   12 | 1   5   3
--------------------+-----+-------+-------------+-------------------+-----------------------+------------------------+----------
x3o3o . .    . .  & ♦   4 |     6 |     4     0 | 2160N     *     * |    2     2    0     0 |   2   1    2    1    0 | 2   2   0
x3o . . x    . .  & ♦   6 |     9 |     2     3 |     * 4320N     * |    0     2    1     2 |   2   0    1    2    3 | 1   3   1
x . . . x    . x    ♦   8 |    12 |     0     6 |     *     * 1080N |    0     0    0     6 |   0   0    0    3    6 | 0   3   2
--------------------+-----+-------+-------------+-------------------+-----------------------+------------------------+----------
x3o3o3o .    . .  & ♦   5 |    10 |    10     0 |     5     0     0 | 864N     *    *     * |   1   1    1    0    0 | 2   1   0
x3o3o . x    . .  & ♦   8 |    16 |     8     6 |     2     4     0 |    * 2160N    *     * |   1   0    1    1    0 | 1   2   0
x3o . o3x    . .  & ♦   9 |    18 |     6     9 |     0     6     0 |    *     * 720N     * |   2   0    0    0    2 | 1   2   1
x3o . . x    . x  & ♦  12 |    24 |     4    15 |     0     4     3 |    *     *    * 2160N |   0   0    0    1    2 | 0   2   1
--------------------+-----+-------+-------------+-------------------+-----------------------+------------------------+----------
x3o3o3o3x    . .  & ♦  30 |   120 |   120    90 |    60   120     0 |   12    30   20     0 | 72N   *    *    *    * | 1   1   0
x3o3o3o . *c3o .  & ♦  10 |    40 |    80     0 |    80     0     0 |   32     0    0     0 |   * 27N    *    *    * | 2   0   0
x3o3o3o .    . x  & ♦  10 |    25 |    20    10 |    10    10     0 |    2     5    0     0 |   *   * 432N    *    * | 1   1   0
x3o3o . x    . x  & ♦  16 |    40 |    16    28 |     4    16     6 |    0     4    0     4 |   *   *    * 540N    * | 0   2   0
x3o . o3x    . x  & ♦  18 |    45 |    12    36 |     0    18     9 |    0     0    2     6 |   *   *    *    * 720N | 0   1   1
--------------------+-----+-------+-------------+-------------------+-----------------------+------------------------+----------
x3o3o3o3x *c3o .  & ♦ 270 |  2160 |  4320  2160 |  4320  4320     0 | 1728  2160  720     0 |  72  54  432    0    0 | N   *   *
x3o3o3o3x    . x  & ♦  60 |   270 |   240   300 |   120   360    90 |   24   120   40   120 |   2   0   12   30   20 | * 36N   *
x3o . o3x   o3x     ♦  27 |    81 |    27    81 |     0    54    27 |    0     0    9    27 |   0   0    0    0    9 | *   * 80N