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

o3x3o3x3o *c3x3o   (N → ∞)

. . . . .    . .    | 1080N |    12 |     6     6    24 |    3    24    12    16 |   12    6    24   8 |   3  12   12 | 6   2
--------------------+-------+-------+-------------------+------------------------+---------------------+--------------+------
. x . . .    . .  & |     2 | 6480N |     1     1     4 |    1     6     4     4 |    6    2     8   4 |   2   8    5 | 5   1
--------------------+-------+-------+-------------------+------------------------+---------------------+--------------+------
o3x . . .    . .  & |     3 |     3 | 2160N     *     * |    1     4     0     0 |    4    2     4   0 |   2   4    4 | 4   1
. x3o . .    . .  & |     3 |     3 |     * 2160N     * |    1     0     4     0 |    6    0     0   4 |   2   8    0 | 5   0
. x . x .    . .  & |     4 |     4 |     *     * 6480N |    0     2     1     2 |    2    1     5   2 |   1   5    4 | 4   1
--------------------+-------+-------+-------------------+------------------------+---------------------+--------------+------
o3x3o . .    . .  & ♦     6 |    12 |     4     4     0 | 540N     *     *     * |    4    0     0   0 |   2   4    0 | 4   0
o3x . x .    . .  & ♦     6 |     9 |     2     0     3 |    * 4320N     *     * |    1    1     2   0 |   1   2    3 | 3   1
. x3o3x .    . .  & ♦    12 |    24 |     0     8     6 |    *     * 1080N     * |    2    0     0   2 |   1   5    0 | 4   0
. x . x .    x .    ♦     8 |    12 |     0     0     6 |    *     *     * 2160N |    0    0     3   1 |   0   3    3 | 3   1
--------------------+-------+-------+-------------------+------------------------+---------------------+--------------+------
o3x3o3x .    . .  & ♦    30 |    90 |    20    30    30 |    5    10     5     0 | 432N    *     *   * |   1   2    0 | 3   0
o3x . x3o    . .  & ♦     9 |    18 |     6     0     9 |    0     6     0     0 |    * 720N     *   * |   1   0    2 | 2   1
o3x . x .    x .  & ♦    12 |    24 |     4     0    15 |    0     4     0     3 |    *    * 2160N   * |   0   1    2 | 2   1
. x3o3x . *c3x .    ♦    96 |   288 |     0    96   144 |    0     0    24    24 |    *    *     * 90N |   0   3    0 | 3   0
--------------------+-------+-------+-------------------+------------------------+---------------------+--------------+------
o3x3o3x3o    . .  & ♦    90 |   360 |   120   120   180 |   30   120    30     0 |   12   20     0   0 | 36N   *    * | 2   0
o3x3o3x . *c3x .  & ♦   480 |  1920 |   320   640  1200 |   80   320   200   240 |   32    0    80  10 |   * 27N    * | 2   0
o3x . x3o    x .  & ♦    18 |    45 |    12     0    36 |    0    18     0     9 |    0    2     6   0 |   *   * 720N | 1   1
--------------------+-------+-------+-------------------+------------------------+---------------------+--------------+------
o3x3o3x3o *c3x .  & ♦  6480 | 32400 |  8640 10800 25920 | 2160 12960  4320  6480 | 1296 1440  4320 270 |  72  54  720 | N   *
o3x . x3o    x3o    ♦    27 |    81 |    27     0    81 |    0    54     0    27 |    0    9    27   0 |   0   0    9 | * 80N