Acronym ...
Name general tetrahedral-octahedral honeycomb variant ao3bo3ob3oa3*a&#zc (but not ao3bo3oa3ob3*a&#zc)
Especially octet (a = b)
Confer
general polytopal classes:
isogonal  

This isogonal honeycomb can 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 o3o3b and each b3a3o gets replaced by a concentrical o3o3a. Then inbetween each pair of parallel but inverted regular triangles of the same size an according trigonal antiprism gets inserted. And inbetween each edge of the new tetrahedron and the intersection of the according ditrigons above a disphenoid ao2ob&#c comes in as well.


Incidence matrix according to Dynkin symbol

ao3bo3ob3oa3*a&#zc   (N → ∞)   → height = 0
                                 c = sqrt[(3a2+2ab+3b2)/8]
(tegum sum of 2 (wrt. the diagram) reflected (a,b)-batatohs)

o.3o.3o.3o.3*a     & | 4N |  3  3   6 |  3  3   9   9 | 1 1  6  3  3
---------------------+----+-----------+---------------+-------------
a. .. .. ..        & |  2 | 6N  *   * |  2  0   2   0 | 1 0  1  2  0
.. b. .. ..        & |  2 |  * 6N   * |  0  2   0   2 | 0 1  1  0  2
oo3oo3oo3oo3*a&#c    |  2 |  *  * 12N |  0  0   2   2 | 0 0  2  1  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  0  1
ao .. .. ..   &#c  & |  3 |  1  0   2 |  *  * 12N   * | 0 0  1  1  0
.. bo .. ..   &#c  & |  3 |  0  1   2 |  *  *   * 12N | 0 0  1  0  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 .. ob ..   &#c  & |  4 |  1  1   4 |  0  0   2   2 | * * 6N  *  * disphenoid
ao .. .. oa3*a&#c    |  6 |  6  0   6 |  2  0   6   0 | * *  * 2N  * (a,c)-trap
.. bo3ob ..   &#c    |  6 |  0  6   6 |  0  2   0   6 | * *  *  * 2N (b,c)-trap

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