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

Remember that gytoh can be seen as a dissection of octet into monostratic slabs, cutting along inscribed trats, and re-adjoining those the other way round. Accordingly the periodicity of gytoh then is about bistratic slabs. Remember furthermore that the rectification of octet is just rich. Then it becomes evident, that it too can be dissected into bistratic slabs, now along inscribed thats. Therefore it becomes evident that this honeycomb under consideration here will have a periodicity of a tetrastratic slab, as is given below. In fact, 2 of the former bistratic slabs will get re-adjoined the other way in here.

Within either of these bistratic slabs the coes of rich remain untouched. While at the re-adjoinment border those become the tobcues of gyrich instead. Therefore this honeycomb happens to be a no longer uniform mixture of rich and gyrich, in fact it has 2 different vertex types: the vertex layers of the medial sections of the coes and the vertex layers of the medial sections of the tobcues, within alternating order.

While the vertex figure of rich is a longer square prism x4o q, the one being used by gyrich in fact is its diametral dissection along an inscribed x h rectangle and then re-adjoining those triangular pyramids at that face the other way round, thus becoming a (xxqq)-kite prism of hight x instead. Both of these vertex figures are being used in here.

Incidence matrix according to Dynkin symbol

:oxxx:3:xxox:3:xoxo:3*a&##xt   (N → ∞)   → all heights = sqrt(2/3) = 0.816497

 o... 3 o... 3 o... 3*a     | 3N  *  *  * |  2  2  2  0  0  0  0  0  0  0  0  2 | 1 1  1  2  2 0 0  0  0  0 0 0  0  0  0 0 0  1  2  2 | 1 1 0 0 0 1 1 2  verf: (xxqq)-kite prism
 .o.. 3 .o.. 3 .o.. 3*a     |  * 3N  *  * |  0  0  2  2  2  2  0  0  0  0  0  0 | 0 0  2  2  1 1 1  2  2  1 0 0  0  0  0 0 0  0  0  0 | 2 1 1 1 0 0 0 1  verf: (xqxq)-rectangular prism
 ..o. 3 ..o. 3 ..o. 3*a     |  *  * 3N  * |  0  0  0  0  0  2  2  2  2  0  0  0 | 0 0  0  0  0 0 0  2  1  2 1 1  2  1  2 0 0  0  0  0 | 1 0 1 2 1 1 0 0  verf: (xxqq)-kite prism
 ...o 3 ...o 3 ...o 3*a     |  *  *  * 3N |  0  0  0  0  0  0  0  0  2  2  2  2 | 0 0  0  0  0 0 0  0  0  0 0 0  2  2  1 1 1  2  2  1 | 0 0 0 1 1 2 1 1  verf: (xqxq)-rectangular prism
----------------------------+-------------+-------------------------------------+-----------------------------------------------------+----------------
 ....   x...   ....         |  2  0  0  0 | 3N  *  *  *  *  *  *  *  *  *  *  * | 1 0  0  1  0 0 0  0  0  0 0 0  0  0  0 0 0  0  1  0 | 1 0 0 0 0 1 0 1
 ....   ....   x...         |  2  0  0  0 |  * 3N  *  *  *  *  *  *  *  *  *  * | 0 1  0  0  1 0 0  0  0  0 0 0  0  0  0 0 0  0  0  1 | 0 1 0 0 0 0 1 1
 oo.. 3 oo.. 3 oo.. 3*a&#x  |  1  1  0  0 |  *  * 6N  *  *  *  *  *  *  *  *  * | 0 0  1  1  1 0 0  0  0  0 0 0  0  0  0 0 0  0  0  0 | 1 1 0 0 0 0 0 1
 .x..   ....   ....         |  0  2  0  0 |  *  *  * 3N  *  *  *  *  *  *  *  * | 0 0  1  0  0 1 0  1  0  0 0 0  0  0  0 0 0  0  0  0 | 1 1 0 1 0 0 0 0
 ....   .x..   ....         |  0  2  0  0 |  *  *  *  * 3N  *  *  *  *  *  *  * | 0 0  0  1  0 0 1  0  1  0 0 0  0  0  0 0 0  0  0  0 | 1 0 1 0 0 0 0 1
 .oo. 3 .oo. 3 .oo. 3*a&#x  |  0  1  1  0 |  *  *  *  *  * 6N  *  *  *  *  *  * | 0 0  0  0  0 0 0  1  1  1 0 0  0  0  0 0 0  0  0  0 | 1 0 1 1 0 0 0 0
 ..x.   ....   ....         |  0  0  2  0 |  *  *  *  *  *  * 3N  *  *  *  *  * | 0 0  0  0  0 0 0  1  0  0 1 0  1  0  0 0 0  0  0  0 | 1 0 0 1 0 1 0 0
 ....   ....   ..x.         |  0  0  2  0 |  *  *  *  *  *  *  * 3N  *  *  *  * | 0 0  0  0  0 0 0  0  0  1 0 1  0  0  1 0 0  0  0  0 | 0 0 1 1 1 0 0 0
 ..oo 3 ..oo 3 ..oo 3*a&#x  |  0  0  1  1 |  *  *  *  *  *  *  *  * 6N  *  *  * | 0 0  0  0  0 0 0  0  0  0 0 0  1  1  1 0 0  0  0  0 | 0 0 0 1 1 1 0 0
 ...x   ....   ....         |  0  0  0  2 |  *  *  *  *  *  *  *  *  * 3N  *  * | 0 0  0  0  0 0 0  0  0  0 0 0  1  0  0 1 0  1  0  0 | 0 0 0 1 0 1 1 0
 ....   ...x   ....         |  0  0  0  2 |  *  *  *  *  *  *  *  *  *  * 3N  * | 0 0  0  0  0 0 0  0  0  0 0 0  0  1  0 0 1  0  1  0 | 0 0 0 0 1 1 0 1
:o..o:3:o..o:3:o..o:3*a&#x  |  1  0  0  1 |  *  *  *  *  *  *  *  *  *  *  * 6N | 0 0  0  0  0 0 0  0  0  0 0 0  0  0  0 0 0  1  1  1 | 0 0 0 0 0 1 1 1
----------------------------+-------------+-------------------------------------+-----------------------------------------------------+----------------
 o... 3 x...   ....         |  3  0  0  0 |  3  0  0  0  0  0  0  0  0  0  0  0 | N *  *  *  * * *  *  *  * * *  *  *  * * *  *  *  * | 1 0 0 0 0 1 0 0
 o...   ....   x... 3*a     |  3  0  0  0 |  0  3  0  0  0  0  0  0  0  0  0  0 | * N  *  *  * * *  *  *  * * *  *  *  * * *  *  *  * | 0 1 0 0 0 0 1 0
 ox..   ....   ....    &#x  |  1  2  0  0 |  0  0  2  1  0  0  0  0  0  0  0  0 | * * 3N  *  * * *  *  *  * * *  *  *  * * *  *  *  * | 1 1 0 0 0 0 0 0
 ....   xx..   ....    &#x  |  2  2  0  0 |  1  0  2  0  1  0  0  0  0  0  0  0 | * *  * 3N  * * *  *  *  * * *  *  *  * * *  *  *  * | 1 0 0 0 0 0 0 1
 ....   ....   xo..    &#x  |  2  1  0  0 |  0  1  2  0  0  0  0  0  0  0  0  0 | * *  *  * 3N * *  *  *  * * *  *  *  * * *  *  *  * | 0 1 0 0 0 0 0 1
 .x..   ....   .o.. 3*a     |  0  3  0  0 |  0  0  0  3  0  0  0  0  0  0  0  0 | * *  *  *  * N *  *  *  * * *  *  *  * * *  *  *  * | 0 1 0 1 0 0 0 0
 ....   .x.. 3 .o..         |  0  3  0  0 |  0  0  0  0  3  0  0  0  0  0  0  0 | * *  *  *  * * N  *  *  * * *  *  *  * * *  *  *  * | 0 0 1 0 0 0 0 1
 .xx.   ....   ....    &#x  |  0  2  2  0 |  0  0  0  1  0  2  1  0  0  0  0  0 | * *  *  *  * * * 3N  *  * * *  *  *  * * *  *  *  * | 1 0 0 1 0 0 0 0
 ....   .xo.   ....    &#x  |  0  2  1  0 |  0  0  0  0  1  2  0  0  0  0  0  0 | * *  *  *  * * *  * 3N  * * *  *  *  * * *  *  *  * | 1 0 1 0 0 0 0 0
 ....   ....   .ox.    &#x  |  0  1  2  0 |  0  0  0  0  0  2  0  1  0  0  0  0 | * *  *  *  * * *  *  * 3N * *  *  *  * * *  *  *  * | 0 0 1 1 0 0 0 0
 ..x. 3 ..o.   ....         |  0  0  3  0 |  0  0  0  0  0  0  3  0  0  0  0  0 | * *  *  *  * * *  *  *  * N *  *  *  * * *  *  *  * | 1 0 0 0 0 1 0 0
 ....   ..o. 3 ..x.         |  0  0  3  0 |  0  0  0  0  0  0  0  3  0  0  0  0 | * *  *  *  * * *  *  *  * * N  *  *  * * *  *  *  * | 0 0 1 0 1 0 0 0
 ..xx   ....   ....    &#x  |  0  0  2  2 |  0  0  0  0  0  0  1  0  2  1  0  0 | * *  *  *  * * *  *  *  * * * 3N  *  * * *  *  *  * | 0 0 0 1 0 1 0 0
 ....   ..ox   ....    &#x  |  0  0  1  2 |  0  0  0  0  0  0  0  0  2  0  1  0 | * *  *  *  * * *  *  *  * * *  * 3N  * * *  *  *  * | 0 0 0 0 1 1 0 0
 ....   ....   ..xo    &#x  |  0  0  2  1 |  0  0  0  0  0  0  0  1  2  0  0  0 | * *  *  *  * * *  *  *  * * *  *  * 3N * *  *  *  * | 0 0 0 1 1 0 0 0
 ...x   ....   ...o 3*a     |  0  0  0  3 |  0  0  0  0  0  0  0  0  0  3  0  0 | * *  *  *  * * *  *  *  * * *  *  *  * N *  *  *  * | 0 0 0 1 0 0 1 0
 ....   ...x 3 ...o         |  0  0  0  3 |  0  0  0  0  0  0  0  0  0  0  3  0 | * *  *  *  * * *  *  *  * * *  *  *  * * N  *  *  * | 0 0 0 0 1 0 0 1
:o..x:  ....   ....    &#x  |  1  0  0  2 |  0  0  0  0  0  0  0  0  0  1  0  2 | * *  *  *  * * *  *  *  * * *  *  *  * * * 3N  *  * | 0 0 0 0 0 1 1 0
 ....  :x..x:  ....    &#x  |  2  0  0  2 |  1  0  0  0  0  0  0  0  0  0  1  2 | * *  *  *  * * *  *  *  * * *  *  *  * * *  * 3N  * | 0 0 0 0 0 1 0 1
 ....   ....  :x..o:   &#x  |  2  0  0  1 |  0  1  0  0  0  0  0  0  0  0  0  2 | * *  *  *  * * *  *  *  * * *  *  *  * * *  *  * 3N | 0 0 0 0 0 0 1 1
----------------------------+-------------+-------------------------------------+-----------------------------------------------------+----------------
 oxx. 3 xxo.   ....    &#xt ♦  3  6  3  0 |  3  0  6  3  3  6  3  0  0  0  0  0 | 1 0  3  3  0 0 0  3  3  0 1 0  0  0  0 0 0  0  0  0 | N * * * * * * *
 ox..   ....   xo.. 3*a&#x  ♦  3  3  0  0 |  0  3  6  3  0  0  0  0  0  0  0  0 | 0 1  3  0  3 1 0  0  0  0 0 0  0  0  0 0 0  0  0  0 | * N * * * * * *
 ....   .xo. 3 .ox.    &#x  ♦  0  3  3  0 |  0  0  0  0  3  6  0  3  0  0  0  0 | 0 0  0  0  0 0 1  0  3  3 0 1  0  0  0 0 0  0  0  0 | * * N * * * * *
 .xxx   ....   .oxo 3*a&#xt ♦  0  3  6  3 |  0  0  0  3  0  6  3  3  6  3  0  0 | 0 0  0  0  0 1 0  3  0  3 0 0  3  0  3 1 0  0  0  0 | * * * N * * * *
 ....   ..ox 3 ..xo    &#x  ♦  0  0  3  3 |  0  0  0  0  0  0  0  3  6  0  3  0 | 0 0  0  0  0 0 0  0  0  0 0 1  0  3  3 0 1  0  0  0 | * * * * N * * *
:o.xx:3:x.ox:  ....    &#xt ♦  3  0  3  6 |  3  0  0  0  0  0  3  0  6  3  3  6 | 1 0  0  0  0 0 0  0  0  0 1 0  3  3  0 0 0  3  3  0 | * * * * * N * *
:o..x:  ....  :x..o:   &#x  ♦  3  0  0  3 |  0  3  0  0  0  0  0  0  0  3  0  6 | 0 1  0  0  0 0 0  0  0  0 0 0  0  0  0 1 0  3  0  3 | * * * * * * N *
 ....  :xx.x:3:xo.o:   &#xt ♦  6  3  0  3 |  3  3  6  0  3  0  0  0  0  0  3  6 | 0 0  0  3  3 0 1  0  0  0 0 0  0  0  0 0 1  0  3  3 | * * * * * * * N