Just as octet itself was the metrical alternation of chon, this isogonal honeycomb is the metrical alternation of the (x,y)-chon variant x4o3o4y. In fact, just let a = xq and b = yq be the diagonals of the different square types, and let c = sqrt(x²+y²) be the diagonal of the according rectangle.

This isogonal honeycomb can also be obtained from an (a,b)-batatoh by keeping its a-tets and b-tets, but by inserting further such tets at the positions of the former tuts. In fact each a3b3o gets replaced by a concentrical o3o3a and each b3a3o gets replaced by a concentrical o3o3b. Then inbetween each pair of parallel but inverted regular triangles of different sizes an according trigonal antipodium gets inserted. And inbetween each edge of the new tetrahedron and the intersection of the according ditrigons above an according disphenoid comes in as well.

Incidence matrix according to Dynkin symbol

ao3bo3oa3ob3*a&#zc   (N → ∞)   → height = 0
                                 c = sqrt[(a2+b2)/2]
(tegum sum of 2 (wrt. the diagram) cyclically rotated (a,b)-batatohs)

o.3o.3o.3o.3*a     & | 4N |  3  3   6 |  3  3   9   9 | 1 1  3  6  3
---------------------+----+-----------+---------------+-------------
a. .. .. ..        & |  2 | 6N  *   * |  2  0   2   0 | 1 0  1  2  0
.. b. .. ..        & |  2 |  * 6N   * |  0  2   0   2 | 0 1  0  2  1
oo3oo3oo3oo3*a&#c    |  2 |  *  * 12N |  0  0   2   2 | 0 0  1  2  1
---------------------+----+-----------+---------------+-------------
a. .. .. o.3*a     & |  3 |  3  0   0 | 4N  *   *   * | 1 0  0  1  0
.. b.3o. ..        & |  3 |  0  3   0 |  * 4N   *   * | 0 1  0  1  0
ao .. .. ..   &#c  & |  3 |  1  0   2 |  *  * 12N   * | 0 0  1  1  0
.. bo .. ..   &#c  & |  3 |  0  1   2 |  *  *   * 12N | 0 0  0  1  1
---------------------+----+-----------+---------------+-------------
a. .. o.3o.3*a     & |  4 |  6  0   0 |  4  0   0   0 | N *  *  *  * a-tet
.. b.3o.3o.        & |  4 |  0  6   0 |  0  4   0   0 | * N  *  *  * b-tet
ao .. oa ..   &#c    |  4 |  2  0   4 |  0  0   4   0 | * * 3N  *  * (a,c)-disphenoid
ao .. .. ob3*a&#c  & |  6 |  3  3   6 |  1  1   3   3 | * *  * 4N  * triangular antipodium
.. bo .. ob   &#c    |  4 |  0  2   4 |  0  0   0   4 | * *  *  * 3N (b,c)-disphenoid