Template:A8 honeycombs
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This honeycomb is one of 45 unique uniform honeycombs[1] constructed by the [math]\displaystyle{ {\tilde{A}}_8 }[/math] Coxeter group. The symmetry can be multiplied by the ring symmetry of the Coxeter diagrams:
A8 honeycombs | ||||
---|---|---|---|---|
Enneagon symmetry |
Symmetry | Extended diagram |
Extended group |
Honeycombs |
a1 | [3[9]] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
[math]\displaystyle{ {\tilde{A}}_8 }[/math] |
|
i2 | [[3[9]]] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
[math]\displaystyle{ {\tilde{A}}_8 }[/math]×2 |
|
i6 | [3[3[9]]] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
[math]\displaystyle{ {\tilde{A}}_8 }[/math]×6 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
r18 | [9[3[9]]] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
[math]\displaystyle{ {\tilde{A}}_8 }[/math]×18 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
References
- ↑ * Weisstein, Eric W.. "Necklace". http://mathworld.wolfram.com/Necklace.html., OEIS sequence A000029 46-1 cases, skipping one with zero marks