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 *c3o3o   (N → ∞)

. . . . .    . .    | 27N |   32 |   160   80 |   320   320 |   80   320  160   80 |  40  20  160   32 | 10  2  32
--------------------+-----+------+------------+-------------+----------------------+-------------------+----------
x . . . .    . .  & |   2 | 432N |    10    5 |    30    30 |   10    40   20   10 |  10   5   25    5 |  5  1   6
--------------------+-----+------+------------+-------------+----------------------+-------------------+----------
x3o . . .    . .  & |   3 |    3 | 1440N    * |     6     2 |    3     6    6    1 |   3   3    6    2 |  3  1   2
x . . . x    . .    |   4 |    4 |     * 540N |     0     8 |    0    12    0    4 |   6   0    8    0 |  4  0   2
--------------------+-----+------+------------+-------------+----------------------+-------------------+----------
x3o3o . .    . .  & ♦   4 |    6 |     4    0 | 2160N     * |    1     1    2    0 |   1   2    2    1 |  2  1   1
x3o . . x    . .  & ♦   6 |    9 |     2    3 |     * 1440N |    0     3    0    1 |   3   0    3    0 |  3  0   1
--------------------+-----+------+------------+-------------+----------------------+-------------------+----------
x3o3o3o .    . .  & ♦   5 |   10 |    10    0 |     5     0 | 432N     *    *    * |   1   2    0    0 |  2  1   0
x3o3o . x    . .  & ♦   8 |   16 |     8    6 |     2     4 |    * 1080N    *    * |   1   0    2    0 |  2  0   1
x3o3o . . *c3o .  & ♦   5 |   10 |    10    0 |     5     0 |    *     * 864N    * |   0   1    1    1 |  1  1   1
x3o . o3x    . .    ♦   9 |   18 |     6    9 |     0     6 |    *     *    * 240N |   3   0    0    0 |  3  0   0
--------------------+-----+------+------------+-------------+----------------------+-------------------+----------
x3o3o3o3x    . .    ♦  30 |  120 |   120   90 |    60   120 |   12    30    0   20 | 36N   *    *    * |  2  0   0
x3o3o3o . *c3o .  & ♦  10 |   40 |    80    0 |    80     0 |   16     0   16    0 |   * 54N    *    * |  1  1   0
x3o3o . x *c3o .  & ♦  10 |   25 |    20   10 |    10    10 |    0     5    2    0 |   *   * 432N    * |  1  0   1
x3o3o . . *c3o3o  & ♦   6 |   15 |    20    0 |    15     0 |    0     0    6    0 |   *   *    * 144N |  0  1   1
--------------------+-----+------+------------+-------------+----------------------+-------------------+----------
x3o3o3o3x *c3o .    ♦ 270 | 2160 |  4320 2160 |  4320  4320 |  864  2160  864  720 |  72  54  432    0 |  N  *   *
x3o3o3o . *c3o3o  & ♦  27 |  216 |   720    0 |  1080     0 |  216     0  432    0 |   0  27    0   72 |  * 2N   *
x3o3o . x *c3o3o  & ♦  12 |   36 |    40   15 |    30    20 |    0    15   12    0 |   0   0    6    2 |  *  * 72N