Acronym etoh
Name elongated tetrahedral-octahedral honeycomb,
elongated alternated cubic honeycomb
 
 © ©    ©
Confer
related CRF honeycombs:
gyeditoh   5Y4-4T-6P3-tri-0  
External
links
wikipedia   polytopewiki

Combining each tet with its adjacent trip into an etripy would result in gyeditoh. – If conversely 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

elong( x3o3o *b4o ),
elong( x3o3o3o3*a )   (N → ∞)

 2N |  3  6 1 |  9  3  3  6 |  4 3  6
----+---------+-------------+--------
  2 | 3N  * * |  4  0  0  0 |  2 2  0
  2 |  * 6N * |  1  1  1  1 |  1 1  2
  2 |  *  * N |  0  0  0  6 |  0 0  6
----+---------+-------------+--------
  3 |  2  1 0 | 6N  *  *  * |  1 1  0
  3 |  0  3 0 |  * 2N  *  * |  1 0  1
  3 |  0  3 0 |  *  * 2N  * |  0 1  1
  4 |  0  2 2 |  *  *  * 3N |  0 0  2
----+---------+-------------+--------
 4 |  3  3 0 |  3  1  0  0 | 2N *  *
 6 |  6  6 0 |  6  0  2  0 |  * N  *
 6 |  0  6 3 |  0  1  1  3 |  * * 2N

:xxoooo:3:ooxxoo:3:ooooxx:3*a&##x   (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 3  6  6  3 0 0  0  0 0 0  0 0 0  0  0 0 0  0 0 0 | 3 3 3 3 1 0 0 0 0 0 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 0  6  0  0 3 3  6  3 0 0  0 0 0  0  0 0 0  0 0 0 | 3 3 0 0 0 3 3 1 0 0 0 0 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 0 0  3  6 3 3  6 0 0  0  0 0 0  0 0 0 | 0 0 0 0 0 3 1 3 3 3 0 0 0 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  0 0 0  6 3 3  6  3 0 0  0 0 0 | 0 0 0 0 0 0 0 0 3 3 3 1 3 0 0
 ....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 0  0 0 0  3  6 3 3  6 0 0 | 0 0 0 0 0 0 0 0 0 0 1 3 3 3 3
 .....o 3 .....o 3 .....o 3*a    | * * * * * N |  0 0  3  0  0  0 0  0  0  0 1  6 | 0 0  0  3  6 0 0  0  0 0 0  0 0 0  0  0 0 0  6 3 3 | 0 0 1 3 3 0 0 0 0 0 0 0 0 3 3
---------------------------------+-------------+----------------------------------+----------------------------------------------------+------------------------------
 x.....   ......   ......        | 2 0 0 0 0 0 | 3N *  *  *  *  * *  *  *  * *  * | 1 1  1  1  0 0 0  0  0 0 0  0 0 0  0  0 0 0  0 0 0 | 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0
 oo.... 3 oo.... 3 oo.... 3*a&#x | 1 1 0 0 0 0 |  * N  *  *  *  * *  *  *  * *  * | 0 0  6  0  0 0 0  0  0 0 0  0 0 0  0  0 0 0  0 0 0 | 3 3 0 0 0 0 0 0 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  0  2  2 0 0  0  0 0 0  0 0 0  0  0 0 0  0 0 0 | 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0
 .x....   ......   ......        | 0 2 0 0 0 0 |  * *  * 3N  *  * *  *  *  * *  * | 0 0  1  0  0 1 1  1  0 0 0  0 0 0  0  0 0 0  0 0 0 | 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0
 .oo... 3 .oo... 3 .oo... 3*a&#x | 0 1 1 0 0 0 |  * *  *  * 3N  * *  *  *  * *  * | 0 0  0  0  0 0 0  2  2 0 0  0 0 0  0  0 0 0  0 0 0 | 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0
 ......   ..x...   ......        | 0 0 2 0 0 0 |  * *  *  *  * 3N *  *  *  * *  * | 0 0  0  0  0 0 0  0  1 1 1  1 0 0  0  0 0 0  0 0 0 | 0 0 0 0 0 1 0 1 1 1 0 0 0 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  0 0 0  6 0 0  0  0 0 0  0 0 0 | 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0
 ......   ...x..   ......        | 0 0 0 2 0 0 |  * *  *  *  *  * * 3N  *  * *  * | 0 0  0  0  0 0 0  0  0 0 0  1 1 1  1  0 0 0  0 0 0 | 0 0 0 0 0 0 0 0 1 1 1 0 1 0 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 0  0 0 0  2  2 0 0  0 0 0 | 0 0 0 0 0 0 0 0 0 0 1 1 2 0 0
 ......   ......   ....x.        | 0 0 0 0 2 0 |  * *  *  *  *  * *  *  * 3N *  * | 0 0  0  0  0 0 0  0  0 0 0  0 0 0  0  1 1 1  1 0 0 | 0 0 0 0 0 0 0 0 0 0 0 1 1 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 0  0  0 0 0  6 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
 ......   ......   .....x        | 0 0 0 0 0 2 |  * *  *  *  *  * *  *  *  * * 3N | 0 0  0  0  1 0 0  0  0 0 0  0 0 0  0  0 0 0  1 1 1 | 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1
---------------------------------+-------------+----------------------------------+----------------------------------------------------+------------------------------
 x..... 3 o.....   ......        | 3 0 0 0 0 0 |  3 0  0  0  0  0 0  0  0  0 0  0 | N *  *  *  * * *  *  * * *  * * *  *  * * *  * * * | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
 x.....   ......   o..... 3*a    | 3 0 0 0 0 0 |  3 0  0  0  0  0 0  0  0  0 0  0 | * N  *  *  * * *  *  * * *  * * *  *  * * *  * * * | 0 1 0 1 0 0 0 0 0 0 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 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 0 1 1 0 0 0 0 0 0 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 0 1 1 0 0 0 0 0 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 *  *  * * *  * * *  *  * * *  * * * | 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
 .x....   ......   .o.... 3*a    | 0 3 0 0 0 0 |  0 0  0  3  0  0 0  0  0  0 0  0 | * *  *  *  * * N  *  * * *  * * *  *  * * *  * * * | 0 1 0 0 0 0 1 0 0 0 0 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  * * *  * * *  *  * * *  * * * | 0 0 0 0 0 1 1 0 0 0 0 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 0 1 0 1 0 0 0 0 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 0 1 0 0 1 0 0 0 0 0 0
 ......   ..x... 3 ..o...        | 0 0 3 0 0 0 |  0 0  0  0  0  3 0  0  0  0 0  0 | * *  *  *  * * *  *  * * N  * * *  *  * * *  * * * | 0 0 0 0 0 0 0 1 0 1 0 0 0 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 0 0 0 1 1 0 0 0 0 0
 ...o.. 3 ...x..   ......        | 0 0 0 3 0 0 |  0 0  0  0  0  0 0  3  0  0 0  0 | * *  *  *  * * *  *  * * *  * N *  *  * * *  * * * | 0 0 0 0 0 0 0 0 1 0 1 0 0 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 0 0 0 0 1 0 0 1 0 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 0 0 0 0 1 0 1 0 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 0 0 0 0 1 1 0 0
 ....o.   ......   ....x. 3*a    | 0 0 0 0 3 0 |  0 0  0  0  0  0 0  0  0  3 0  0 | * *  *  *  * * *  *  * * *  * * *  *  * N *  * * * | 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0
 ......   ....o. 3 ....x.        | 0 0 0 0 3 0 |  0 0  0  0  0  0 0  0  0  3 0  0 | * *  *  *  * * *  *  * * *  * * *  *  * * N  * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
 ......   ......   ....xx    &#x | 0 0 0 0 2 2 |  0 0  0  0  0  0 0  0  0  1 2  1 | * *  *  *  * * *  *  * * *  * * *  *  * * * 3N * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 1 0
 ......   .....o 3 .....x        | 0 0 0 0 0 3 |  0 0  0  0  0  0 0  0  0  0 0  3 | * *  *  *  * * *  *  * * *  * * *  *  * * *  * * N | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1
---------------------------------+-------------+----------------------------------+----------------------------------------------------+------------------------------
 xx.... 3 oo....   ......    &#x  3 3 0 0 0 0 |  3 3  0  3  0  0 0  0  0  0 0  0 | 1 0  3  0  0 1 0  0  0 0 0  0 0 0  0  0 0 0  0 0 0 | N * * * * * * * * * * * * * *
 xx....   ......   oo.... 3*a&#x  3 3 0 0 0 0 |  3 3  0  3  0  0 0  0  0  0 0  0 | 0 1  3  0  0 0 1  0  0 0 0  0 0 0  0  0 0 0  0 0 0 | * N * * * * * * * * * * * * *
:x....o:3:o....o: :......:   &#x  3 0 0 0 0 1 |  3 0  3  0  0  0 0  0  0  0 0  0 | 1 0  0  3  0 0 0  0  0 0 0  0 0 0  0  0 0 0  0 0 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 | 0 1  0  3  3 0 0  0  0 0 0  0 0 0  0  0 0 0  0 1 0 | * * * N * * * * * * * * * * *
:......: :o....o:3:o....x:3*a&#x  1 0 0 0 0 3 |  0 0  3  0  0  0 0  0  0  0 0  3 | 0 0  0  0  3 0 0  0  0 0 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  0 1 0  3  3 1 0  0 0 0  0  0 0 0  0 0 0 | * * * * * N * * * * * * * * *
 .xo...   ......   .oo... 3*a&#x  0 3 1 0 0 0 |  0 0  0  3  3  0 0  0  0  0 0  0 | 0 0  0  0  0 0 1  3  0 0 0  0 0 0  0  0 0 0  0 0 0 | * * * * * * N * * * * * * * *
 ......   .ox... 3 .oo...    &#x  0 1 3 0 0 0 |  0 0  0  0  3  3 0  0  0  0 0  0 | 0 0  0  0  0 0 0  0  3 0 1  0 0 0  0  0 0 0  0 0 0 | * * * * * * * N * * * * * * *
 ..oo.. 3 ..xx..   ......    &#x  0 0 3 3 0 0 |  0 0  0  0  0  3 3  3  0  0 0  0 | 0 0  0  0  0 0 0  0  0 1 0  3 1 0  0  0 0 0  0 0 0 | * * * * * * * * N * * * * * *
 ......   ..xx.. 3 ..oo..    &#x  0 0 3 3 0 0 |  0 0  0  0  0  3 3  3  0  0 0  0 | 0 0  0  0  0 0 0  0  0 0 1  3 0 1  0  0 0 0  0 0 0 | * * * * * * * * * N * * * * *
 ...oo. 3 ...xo.   ......    &#x  0 0 0 3 1 0 |  0 0  0  0  0  0 0  3  3  0 0  0 | 0 0  0  0  0 0 0  0  0 0 0  0 1 0  3  0 0 0  0 0 0 | * * * * * * * * * * N * * * *
 ...oo.   ......   ...ox. 3*a&#x  0 0 0 1 3 0 |  0 0  0  0  0  0 0  0  3  3 0  0 | 0 0  0  0  0 0 0  0  0 0 0  0 0 0  0  3 1 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 0 0  0 0 1  3  3 0 1  0 0 0 | * * * * * * * * * * * * N * *
 ....oo   ......   ....xx 3*a&#x  0 0 0 0 3 3 |  0 0  0  0  0  0 0  0  0  3 3  3 | 0 0  0  0  0 0 0  0  0 0 0  0 0 0  0  0 1 0  3 1 0 | * * * * * * * * * * * * * N *
 ......   ....oo 3 ....xx 3*a&#x  0 0 0 0 3 3 |  0 0  0  0  0  0 0  0  0  3 3  3 | 0 0  0  0  0 0 0  0  0 0 0  0 0 0  0  0 0 1  3 0 1 | * * * * * * * * * * * * * * N

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