This honeycomb is the general form of one of the 3 phases of the tegum sum of 2 inverted general srich variants, ao4ob3bo4oa&#zc, here in fact the realm of 1/sqrt(2) < b:a < 3/sqrt(2). The other ones will be sabirch for 0 < b:a < 1/sqrt(2) resp. gabirch for 3/sqrt(2) < b:a < ∞.

Further there are singular transition cases too. The relevant ones for the current realm are the bordering cases b:a = 1/sqrt(2) (rich) and b:a = 3/sqrt(2) (rebatch) respectively.

Incidence matrix according to Dynkin symbol

ao4ob3bo4oa&#zc   (N → ∞)   → height = 0
                              c = sqrt[3a2-2ab sqrt(2)+2b2]/2
                              1/sqrt(2) < b:a < 3/sqrt(2)

o.4o.3o.4o.     & | 12N |   2   4   4 |   4  2  2   6   6 |  2 1   5  2  2
------------------+-----+-------------+-------------------+---------------
a. .. .. ..     & |   2 | 12N   *   * |   2  0  0   2   0 |  1 0   2  1  0
.. .. b. ..     & |   2 |   * 24N   * |   1  1  1   0   1 |  1 1   1  0  1
oo4oo3oo4oo&#c    |   2 |   *   * 24N |   0  0  0   2   2 |  0 0   2  1  1
------------------+-----+-------------+-------------------+---------------
a. .. b. ..     & |   4 |   2   2   0 | 12N  *  *   *   * |  1 0   1  0  0
.. o.3b. ..     & |   3 |   0   3   0 |   * 8N  *   *   * |  0 1   0  0  1
.. .. b.4o.     & |   4 |   0   4   0 |   *  * 6N   *   * |  1 1   0  0  0
ao .. .. ..&#c  & |   3 |   1   0   2 |   *  *  * 24N   * |  0 0   1  1  0
.. ob .. ..&#c  & |   3 |   0   1   2 |   *  *  *   * 24N |  0 0   1  0  1
------------------+-----+-------------+-------------------+---------------
a. .. b.4o.     & |   8 |   4   8   0 |   4  0  2   0   0 | 3N *   *  *  * (b,a)-4p
.. o.3b.4o.     & |  12 |   0  24   0 |   0  8  6   0   0 |  * N   *  *  * b-co
ao .. bo ..&#c  & |   5 |   2   2   4 |   1  0  0   2   2 |  * * 12N  *  * (a,b,c)-squippy
ao .. .. oa&#c    |   4 |   2   0   4 |   0  0  0   4   0 |  * *   * 6N  * tetragonal disphenoid (tet variant)
.. ob3bo ..&#c    |   6 |   0   6   6 |   0  2  0   0   6 |  * *   *  * 4N (b,c)-3ap