Acronym	gytoh
Name	gyrated tetrahedral-octahedral honeycomb, gyrated alternated cubic honeycomb
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Confer	related tesselations: octet   gyetoh   related CRF honeycombs: ditoh   10Y4-8T-3   rigytoh   ambification: rigytoh
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Gyration (in parallel trat sections) here makes tets adjacent to tets and octs adjacent to octs. Whereas in the (un-gyrated) octet those would be alternating at any triangle instead.

As this non-Wythoffian honeycomb uses regular triangles all over, it well can get subject of ambification, then resulting in rigytoh.

Incidence matrix according to Dynkin symbol

:xo:3:ox:3:oo:3*a&##x   (N → ∞)   → all heights = sqrt(2/3) = 0.816497

 o. 3 o. 3 o. 3*a    | N * ♦  6  3  0  3 | 3 3  6  3 0 0  6  3 | 3 3 1 3 3 1
 .o 3 .o 3 .o 3*a    | * N ♦  0  3  6  3 | 0 0  3  6 3 3  3  6 | 3 1 3 3 1 3
---------------------+-----+-------------+---------------------+------------
 x.   ..   ..        | 2 0 | 3N  *  *  * | 1 1  1  0 0 0  1  0 | 1 1 0 1 1 0
 oo 3 oo 3 oo 3*a&#x | 1 1 |  * 3N  *  * | 0 0  2  2 0 0  0  0 | 2 1 1 0 0 0
 ..   .x   ..        | 0 2 |  *  * 3N  * | 0 0  0  1 1 1  0  1 | 1 0 1 1 0 1
:oo:3:oo:3:oo:3*a&#x | 1 1 |  *  *  * 3N | 0 0  0  0 0 0  2  2 | 0 0 0 2 1 1
---------------------+-----+-------------+---------------------+------------
 x. 3 o.   ..        | 3 0 |  3  0  0  0 | N *  *  * * *  *  * | 1 0 0 1 0 0
 x.   ..   o. 3*a    | 3 0 |  3  0  0  0 | * N  *  * * *  *  * | 0 1 0 0 1 0
 xo   ..   ..    &#x | 2 1 |  1  2  0  0 | * * 3N  * * *  *  * | 1 1 0 0 0 0
 ..   ox   ..    &#x | 1 2 |  0  2  1  0 | * *  * 3N * *  *  * | 1 0 1 0 0 0
 .o 3 .x   ..        | 0 3 |  0  0  3  0 | * *  *  * N *  *  * | 1 0 0 1 0 0
 ..   .x 3 .o        | 0 3 |  0  0  3  0 | * *  *  * * N  *  * | 0 0 1 0 0 1
:xo:  ..   ..    &#x | 2 1 |  1  0  0  2 | * *  *  * * * 3N  * | 0 0 0 1 1 0
     :ox:  ..    &#x | 1 2 |  0  0  1  2 | * *  *  * * *  * 3N | 0 0 0 1 0 1
---------------------+-----+-------------+---------------------+------------
 xo 3 ox   ..    &#x ♦ 3 3 |  3  6  3  0 | 1 0  3  3 1 0  0  0 | N * * * * *
 xo   ..   oo 3*a&#x ♦ 3 1 |  3  3  0  0 | 0 1  3  0 0 0  0  0 | * N * * * *
 ..   ox 3 oo    &#x ♦ 1 3 |  0  3  3  0 | 0 0  0  3 0 1  0  0 | * * N * * *
:xo:3:ox:  ..    &#x ♦ 3 3 |  3  0  3  6 | 1 0  0  0 1 0  3  3 | * * * N * *
:xo:  ..  :oo:3*a&#x ♦ 3 1 |  3  0  0  3 | 0 1  0  0 0 0  3  0 | * * * * N *
 ..  :ox:3:oo:   &#x ♦ 1 3 |  0  0  3  3 | 0 0  0  0 0 1  0  3 | * * * * * N

or
 o. 3 o. 3 o. 3*a    & | N ♦  6  6 | 3 3 18 | 6  8
-----------------------+---+-------+--------+-----
 x.   ..   ..        & | 2 | 3N  * | 1 1  2 | 2  2
 oo 3 oo 3 oo 3*a&#x & | 2 |  * 3N | 0 0  4 | 2  2
-----------------------+---+-------+--------+-----
 x. 3 o.   ..        & | 3 |  3  0 | N *  * | 2  0
 x.   ..   o. 3*a    & | 3 |  3  0 | * N  * | 0  2
 xo   ..   ..    &#x & | 3 |  1  2 | * * 6N | 1  1
-----------------------+---+-------+--------+-----
 xo 3 ox   ..    &#x & ♦ 6 |  6  6 | 2 0  6 | N  *
 xo   ..   oo 3*a&#x & ♦ 4 |  3  3 | 0 1  3 | * 2N