Difference between revisions of "Template:A4 honeycombs"

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blackwiki>Tomruen
blackwiki>Tomruen
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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=4| A4 honeycombs
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!colspan=5| A4 honeycombs
 
|-
 
|-
|
 
{| class=wikitable
 
 
![[: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}}&nbsp;<sub>[[Omnitruncated 5-cell honeycomb|7]]</sub>
 
|{{CDD|node_1|split1|nodes_11|3ab|branch_11}}&nbsp;<sub>[[Omnitruncated 5-cell honeycomb|7]]</sub>
|}
 
 
|}<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:

References

  1. [1], A000029 8-1 cases, skipping one with zero marks