Difference between revisions of "Template:A4 honeycombs"
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This honeycomb is one of [[Uniform 5-polytope#Regular and uniform honeycombs|seven unique uniform honeycombs]]<ref>[http://mathworld.wolfram.com/Necklace.html], [http://oeis.org/A000029 A000029] 8-1 cases, skipping one with zero marks</ref> constructed by the <math>{\tilde{A}}_4</math> [[Coxeter group]]. The symmetry can be multiplied by the symmetry of rings in the [[Coxeter–Dynkin diagram]]s: | This honeycomb is one of [[Uniform 5-polytope#Regular and uniform honeycombs|seven unique uniform honeycombs]]<ref>[http://mathworld.wolfram.com/Necklace.html], [http://oeis.org/A000029 A000029] 8-1 cases, skipping one with zero marks</ref> constructed by the <math>{\tilde{A}}_4</math> [[Coxeter group]]. The symmetry can be multiplied by the symmetry of rings in the [[Coxeter–Dynkin diagram]]s: | ||
{| class="wikitable collapsible collapsed" | {| class="wikitable collapsible collapsed" | ||
| − | !colspan= | + | !colspan=5| A4 honeycombs |
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![[:File:Symmetries_of_pentagon.png|Pentagon<BR>symmetry]] | ![[:File:Symmetries_of_pentagon.png|Pentagon<BR>symmetry]] | ||
![[Coxeter notation|Extended<BR>symmetry]] | ![[Coxeter notation|Extended<BR>symmetry]] | ||
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| <math>{\tilde{A}}_4</math>×10 | | <math>{\tilde{A}}_4</math>×10 | ||
|{{CDD|node_1|split1|nodes_11|3ab|branch_11}} <sub>[[Omnitruncated 5-cell honeycomb|7]]</sub> | |{{CDD|node_1|split1|nodes_11|3ab|branch_11}} <sub>[[Omnitruncated 5-cell honeycomb|7]]</sub> | ||
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|}<noinclude> | |}<noinclude> | ||
Revision as of 20:55, 19 February 2016
This honeycomb is one of seven unique uniform honeycombs[1] constructed by the <math>{\tilde{A}}_4</math> Coxeter group. The symmetry can be multiplied by the symmetry of rings in the Coxeter–Dynkin diagrams: