This honeycomb is the general form of one of the 2 phases of the tegum sum of 2 inverted general rich variants, ao3ob3bo3oa3*a&#zc, here in fact the realm of 1 ≤ b:a < 3. The other one will be gobath for 3 < b:a < ∞.

Further there are singular transition cases too. The relevant ones for the current realm are the bordering cases case b:a = 1 (same topology, just special size ratio and thus higher symmetry) and case b:a = 3.

Incidence matrix according to Dynkin symbol

ao3ob3bo3oa3*a&#zc   (N → ∞)   →height = 0
                                 c = sqrt[(3a2-2ab+3b2)/8]
                                 1 ≤ b:a < 3 (a ≤ b without loss of generality)
(tegum sum of 2 inverted (a,b)-richs)

o.3o.3o.3o.3*a     & | 6N |   4   4   4 |  2  2  2  2   6   6 | 1 1  4  2  2
---------------------+----+-------------+---------------------+-------------
a. .. .. ..        & |  2 | 12N   *   * |  1  1  0  0   1   0 | 1 0  1  1  0
.. .. b. ..        & |  2 |   * 12N   * |  0  0  1  1   0   1 | 0 1  1  0  1
oo3oo3oo3oo3*a&#c    |  2 |   *   * 12N |  0  0  0  0   2   2 | 0 0  2  1  1
---------------------+----+-------------+---------------------+-------------
a.3o. .. ..        & |  3 |   3   0   0 | 4N  *  *  *   *   * | 1 0  1  0  0
a. .. .. o.3*a     & |  3 |   3   0   0 |  * 4N  *  *   *   * | 1 0  0  1  0
.. o.3b. ..        & |  3 |   0   3   0 |  *  * 4N  *   *   * | 0 1  0  0  1
.. .. b.3o.        & |  3 |   0   3   0 |  *  *  * 4N   *   * | 0 1  1  0  0
ao .. .. ..   &#c  & |  3 |   1   0   2 |  *  *  *  * 12N   * | 0 0  1  1  0
.. ob .. ..   &#c  & |  3 |   0   1   2 |  *  *  *  *   * 12N | 0 0  1  0  1
---------------------+----+-------------+---------------------+-------------
a.3o. .. o.3*a     & |  6 |  12   0   0 |  4  4  0  0   0   0 | N *  *  *  * a-oct
.. o.3b.3o.        & |  6 |   0  12   0 |  0  0  4  4   0   0 | * N  *  *  * b-oct
ao3ob .. ..   &#c  & |  6 |   3   3   6 |  1  0  0  1   3   3 | * * 4N  *  * triangular antipodium
ao .. .. oa3*a&#c    |  6 |   6   0   6 |  0  2  0  0   6   0 | * *  * 2N  * tall trap
.. ob3bo ..   &#c    |  6 |   0   6   6 |  0  0  2  0   0   6 | * *  *  * 2N shallow trap