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 *c3o3o   (N → ∞)

. . . . .    . .    | 540N |    16 |     8    24    16 |    12    16    24    16 |   24    8    4   16    4 |   6  16   2   4 | 4  4
--------------------+------+-------+-------------------+-------------------------+--------------------------+-----------------+-----
. x . . .    . .  & |    2 | 4320N |     1     3     2 |     3     3     6     3 |    9    3    1    6    1 |   3   9   1   2 | 3  3
--------------------+------+-------+-------------------+-------------------------+--------------------------+-----------------+-----
o3x . . .    . .  & |    3 |     3 | 1440N     *     * |     3     2     0     0 |    6    3    1    0    0 |   3   6   1   0 | 3  2
. x3o . .    . .  & |    3 |     3 |     * 4320N     * |     1     0     2     2 |    3    2    0    4    1 |   1   6   1   2 | 2  3
. x . x .    . .    |    4 |     4 |     *     * 2160N |     0     2     3     0 |    6    0    1    3    0 |   3   6   0   1 | 3  2
--------------------+------+-------+-------------------+-------------------------+--------------------------+-----------------+-----
o3x3o . .    . .  & ♦    6 |    12 |     4     4     0 | 1080N     *     *     * |    2    2    0    0    0 |   1   4   1   0 | 2  2
o3x . x .    . .  & ♦    6 |     9 |     2     0     3 |     * 1440N     *     * |    3    0    1    0    0 |   3   3   0   0 | 3  1
. x3o3x .    . .    ♦   12 |    24 |     0     8     6 |     *     * 1080N     * |    2    0    0    2    0 |   1   4   0   1 | 2  2
. x3o . . *c3o .  & ♦    4 |     6 |     0     4     0 |     *     *     * 2160N |    0    1    0    2    1 |   0   3   1   2 | 1  3
--------------------+------+-------+-------------------+-------------------------+--------------------------+-----------------+-----
o3x3o3x .    . .  & ♦   30 |    90 |    20    30    30 |     5    10     5     0 | 432N    *    *    *    * |   1   2   0   0 | 2  1
o3x3o . . *c3o .  & ♦   10 |    30 |    10    20     0 |     5     0     0     5 |    * 432N    *    *    * |   0   2   1   0 | 1  2
o3x . x3o    . .    ♦    9 |    18 |     6     0     9 |     0     6     0     0 |    *    * 240N    *    * |   3   0   0   0 | 3  0
. x3o3x . *c3o .    ♦   32 |    96 |     0    64    24 |     0     0     8    16 |    *    *    * 270N    * |   0   2   0   1 | 1  2
. x3o . . *c3o3o  & ♦    5 |    10 |     0    10     0 |     0     0     0     5 |    *    *    *    * 432N |   0   0   1   2 | 0  3
--------------------+------+-------+-------------------+-------------------------+--------------------------+-----------------+-----
o3x3o3x3o    . .    ♦   90 |   360 |   120   120   180 |    30   120    30     0 |   12    0   20    0    0 | 36N   *   *   * | 2  0
o3x3o3x . *c3o .  & ♦  160 |   720 |   160   480   240 |    80    80    80   120 |   16   16    0   10    0 |   * 54N   *   * | 1  1
o3x3o . . *c3o3o  & ♦   15 |    60 |    20    60     0 |    15     0     0    30 |    0    6    0    0    6 |   *   * 72N   * | 0  2
. x3o3x . *c3o3o    ♦   80 |   320 |     0   320    80 |     0     0    40   160 |    0    0    0   10   32 |   *   *   * 27N | 0  2
--------------------+------+-------+-------------------+-------------------------+--------------------------+-----------------+-----
o3x3o3x3o *c3o .    ♦ 2160 | 12960 |  4320  8640  6480 |  2160  4320  2160  2160 |  864  432  720  270    0 |  72  54   0   0 | N  *
o3x3o3x . *c3o3o  & ♦ 1080 |  6480 |  1440  6480  2160 |  1080   720  1080  3240 |  216  432    0  270  648 |   0  27  72  27 | * 2N