Acronym gyeditoh Name gyroelongated ditetrahedral-octahedral honeycomb Confer uniform relative: etoh   related CRF honeycombs: editoh   5Y4-4T-6P3-tri-0

This CRF honeycomb is the gyrated form of editoh.

Dissecting each etripy into a tet and a trip, then this would result in etoh. – If further all octs would be dissected by parallel planes into pairs of squippies, this honeycomb would become 5Y4-4T-6P3-tri-0.

Incidence matrix according to Dynkin symbol

```(N → ∞)

2N |  3  6 1 |  9  3  6 |  7 3
---+---------+----------+-----
2 | 3N  * * |  4  0  0 |  2 2  obl. lacings
2 |  * 6N * |  1  1  1 |  2 1
2 |  *  * N |  0  0  6 |  6 0  prism lacings
---+---------+----------+-----
3 |  2  1 0 | 6N  *  * |  1 1
3 |  0  3 0 |  * 2N  * |  1 1
4 |  0  2 2 |  *  * 3N |  2 0
---+---------+----------+-----
7 |  3  6 3 |  3  1  3 | 2N *  etripy
6 |  6  6 0 |  6  2  0 |  * N  oct
```

```reduced(:xxoooo:3:ooxxoo:3:ooooxx:3*a&##x, by etripy dissecting {3}s)   (N → ∞)   → heights alternatingly = sqrt(2/3) = 0.816497 resp. = 1

o..... 3 o..... 3 o..... 3*a     | N * * * * * |  6 1  3  0  0  0 0  0  0  0 0  0 | 3  6  6  3 0  0  0 0  0 0  0  0 0  0 0 | 3 3 1 3 0 0 0 0 0
.o.... 3 .o.... 3 .o.... 3*a     | * N * * * * |  0 1  0  6  3  0 0  0  0  0 0  0 | 0  6  0  0 3  6  3 0  0 0  0  0 0  0 0 | 3 3 0 0 3 1 0 0 0
..o... 3 ..o... 3 ..o... 3*a     | * * N * * * |  0 0  0  0  3  6 1  0  0  0 0  0 | 0  0  0  0 0  3  6 3  6 0  0  0 0  0 0 | 1 0 0 0 3 3 3 0 0
...o.. 3 ...o.. 3 ...o.. 3*a     | * * * N * * |  0 0  0  0  0  0 1  6  3  0 0  0 | 0  0  0  0 0  0  0 0  6 3  6  3 0  0 0 | 0 0 0 0 0 3 3 3 1
....o. 3 ....o. 3 ....o. 3*a     | * * * * N * |  0 0  0  0  0  0 0  0  3  6 1  0 | 0  0  0  0 0  0  0 0  0 0  3  6 3  6 0 | 0 0 3 0 0 0 1 3 3
.....o 3 .....o 3 .....o 3*a     | * * * * * N |  0 0  3  0  0  0 0  0  0  0 1  6 | 0  0  3  6 0  0  0 0  0 0  0  0 0  6 3 | 0 1 3 3 0 0 0 0 3
----------------------------------+-------------+----------------------------------+----------------------------------------+------------------
x.....   ......   ......         | 2 0 0 0 0 0 | 3N *  *  *  *  * *  *  *  * *  * | 1  1  1  0 0  0  0 0  0 0  0  0 0  0 0 | 1 1 0 1 0 0 0 0 0
oo.... 3 oo.... 3 oo.... 3*a&#x  | 1 1 0 0 0 0 |  * N  *  *  *  * *  *  *  * *  * | 0  6  0  0 0  0  0 0  0 0  0  0 0  0 0 | 3 3 0 0 0 0 0 0 0
:o....o:3:o....o:3:o....o:3*a&#x  | 1 0 0 0 0 1 |  * * 3N  *  *  * *  *  *  * *  * | 0  0  2  2 0  0  0 0  0 0  0  0 0  0 0 | 0 1 1 2 0 0 0 0 0
.x....   ......   ......         | 0 2 0 0 0 0 |  * *  * 3N  *  * *  *  *  * *  * | 0  1  0  0 1  1  0 0  0 0  0  0 0  0 0 | 1 1 0 0 1 0 0 0 0
.oo... 3 .oo... 3 .oo... 3*a&#x  | 0 1 1 0 0 0 |  * *  *  * 3N  * *  *  *  * *  * | 0  0  0  0 0  2  2 0  0 0  0  0 0  0 0 | 1 0 0 0 2 1 0 0 0
......   ..x...   ......         | 0 0 2 0 0 0 |  * *  *  *  * 3N *  *  *  * *  * | 0  0  0  0 0  0  1 1  1 0  0  0 0  0 0 | 0 0 0 0 1 1 1 0 0
..oo.. 3 ..oo.. 3 ..oo.. 3*a&#x  | 0 0 1 1 0 0 |  * *  *  *  *  * N  *  *  * *  * | 0  0  0  0 0  0  0 0  6 0  0  0 0  0 0 | 0 0 0 0 0 3 3 0 0
......   ...x..   ......         | 0 0 0 2 0 0 |  * *  *  *  *  * * 3N  *  * *  * | 0  0  0  0 0  0  0 0  1 1  1  0 0  0 0 | 0 0 0 0 0 1 1 1 0
...oo. 3 ...oo. 3 ...oo. 3*a&#x  | 0 0 0 1 1 0 |  * *  *  *  *  * *  * 3N  * *  * | 0  0  0  0 0  0  0 0  0 0  2  2 0  0 0 | 0 0 0 0 0 0 1 2 1
......   ......   ....x.         | 0 0 0 0 2 0 |  * *  *  *  *  * *  *  * 3N *  * | 0  0  0  0 0  0  0 0  0 0  0  1 1  1 0 | 0 0 1 0 0 0 0 1 1
....oo 3 ....oo 3 ....oo 3*a&#x  | 0 0 0 0 1 1 |  * *  *  *  *  * *  *  *  * N  * | 0  0  0  0 0  0  0 0  0 0  0  0 0  6 0 | 0 0 3 0 0 0 0 0 3
......   ......   .....x         | 0 0 0 0 0 2 |  * *  *  *  *  * *  *  *  * * 3N | 0  0  0  1 0  0  0 0  0 0  0  0 0  1 1 | 0 0 1 1 0 0 0 0 1
----------------------------------+-------------+----------------------------------+----------------------------------------+------------------
x.....   ......   o..... 3*a     | 3 0 0 0 0 0 |  3 0  0  0  0  0 0  0  0  0 0  0 | N  *  *  * *  *  * *  * *  *  * *  * * | 1 0 0 1 0 0 0 0 0
xx....   ......   ......    &#x  | 2 2 0 0 0 0 |  1 2  0  1  0  0 0  0  0  0 0  0 | * 3N  *  * *  *  * *  * *  *  * *  * * | 1 1 0 0 0 0 0 0 0
:x....o: :......: :......:   &#x  | 2 0 0 0 0 1 |  1 0  2  0  0  0 0  0  0  0 0  0 | *  * 3N  * *  *  * *  * *  *  * *  * * | 0 1 0 1 0 0 0 0 0
:......: :......: :o....x:   &#x  | 1 0 0 0 0 2 |  0 0  2  0  0  0 0  0  0  0 0  1 | *  *  * 3N *  *  * *  * *  *  * *  * * | 0 0 1 1 0 0 0 0 0
.x.... 3 .o....   ......         | 0 3 0 0 0 0 |  0 0  0  3  0  0 0  0  0  0 0  0 | *  *  *  * N  *  * *  * *  *  * *  * * | 0 1 0 0 1 0 0 0 0
.xo...   ......   ......    &#x  | 0 2 1 0 0 0 |  0 0  0  1  2  0 0  0  0  0 0  0 | *  *  *  * * 3N  * *  * *  *  * *  * * | 1 0 0 0 1 0 0 0 0
......   .ox...   ......    &#x  | 0 1 2 0 0 0 |  0 0  0  0  2  1 0  0  0  0 0  0 | *  *  *  * *  * 3N *  * *  *  * *  * * | 0 0 0 0 1 1 0 0 0
..o... 3 ..x...   ......         | 0 0 3 0 0 0 |  0 0  0  0  0  3 0  0  0  0 0  0 | *  *  *  * *  *  * N  * *  *  * *  * * | 0 0 0 0 1 0 1 0 0
......   ..xx..   ......    &#x  | 0 0 2 2 0 0 |  0 0  0  0  0  1 2  1  0  0 0  0 | *  *  *  * *  *  * * 3N *  *  * *  * * | 0 0 0 0 0 1 1 0 0
......   ...x.. 3 ...o..         | 0 0 0 3 0 0 |  0 0  0  0  0  0 0  3  0  0 0  0 | *  *  *  * *  *  * *  * N  *  * *  * * | 0 0 0 0 0 1 0 1 0
......   ...xo.   ......    &#x  | 0 0 0 2 1 0 |  0 0  0  0  0  0 0  1  2  0 0  0 | *  *  *  * *  *  * *  * * 3N  * *  * * | 0 0 0 0 0 0 1 1 0
......   ......   ...ox.    &#x  | 0 0 0 1 2 0 |  0 0  0  0  0  0 0  0  2  1 0  0 | *  *  *  * *  *  * *  * *  * 3N *  * * | 0 0 0 0 0 0 0 1 1
......   ....o. 3 ....x.         | 0 0 0 0 3 0 |  0 0  0  0  0  0 0  0  0  3 0  0 | *  *  *  * *  *  * *  * *  *  * N  * * | 0 0 1 0 0 0 0 1 0
......   ......   ....xx    &#x  | 0 0 0 0 2 2 |  0 0  0  0  0  0 0  0  0  1 2  1 | *  *  *  * *  *  * *  * *  *  * * 3N * | 0 0 1 0 0 0 0 0 1
.....o   ......   .....x 3*a     | 0 0 0 0 0 3 |  0 0  0  0  0  0 0  0  0  0 0  3 | *  *  *  * *  *  * *  * *  *  * *  * N | 0 0 0 1 0 0 0 0 1
----------------------------------+-------------+----------------------------------+----------------------------------------+------------------
xxo...   ......   ooo... 3*a&#xt ♦ 3 3 1 0 0 0 |  3 3  0  3  3  0 0  0  0  0 0  0 | 1  3  0  0 0  3  0 0  0 0  0  0 0  0 0 | N * * * * * * * *
:xx...o:3:oo...o:  ......    &#xt ♦ 3 3 0 0 0 1 |  3 3  3  3  0  0 0  0  0  0 0  0 | 0  3  3  0 1  0  0 0  0 0  0  0 0  0 0 | * N * * * * * * *
:......: :o...oo:3:o...xx:3*a&#xt ♦ 1 0 0 0 3 3 |  0 0  3  0  0  0 0  0  0  3 3  3 | 0  0  0  3 0  0  0 0  0 0  0  0 1  3 0 | * * N * * * * * *
:x....o: :......: :o....x:3*a&#x  ♦ 3 0 0 0 0 3 |  3 0  6  0  0  0 0  0  0  0 0  3 | 1  0  3  3 0  0  0 0  0 0  0  0 0  0 1 | * * * N * * * * *
.xo... 3 .ox...   ......    &#x  ♦ 0 3 3 0 0 0 |  0 0  0  3  6  3 0  0  0  0 0  0 | 0  0  0  0 1  3  3 1  0 0  0  0 0  0 0 | * * * * N * * * *
......   .oxx.. 3 .ooo..    &#xt ♦ 0 1 3 3 0 0 |  0 0  0  0  3  3 3  3  0  0 0  0 | 0  0  0  0 0  0  3 0  3 1  0  0 0  0 0 | * * * * * N * * *
..ooo. 3 ..xxo.   ......    &#xt ♦ 0 0 3 3 1 0 |  0 0  0  0  0  3 3  3  3  0 0  0 | 0  0  0  0 0  0  0 1  3 0  3  0 0  0 0 | * * * * * * N * *
......   ...xo. 3 ...ox.    &#x  ♦ 0 0 0 3 3 0 |  0 0  0  0  0  0 0  3  6  3 0  0 | 0  0  0  0 0  0  0 0  0 1  3  3 1  0 0 | * * * * * * * N *
...ooo   ......   ...oxx 3*a&#xt ♦ 0 0 0 1 3 3 |  0 0  0  0  0  0 0  0  3  3 3  3 | 0  0  0  0 0  0  0 0  0 0  0  3 0  3 1 | * * * * * * * * N
```