View source for Template:A4 honeycombs

This honeycomb is one of [[Uniform 5-polytope#Regular and uniform honeycombs|seven unique uniform honeycombs]]<ref>[http://mathworld.wolfram.com/Necklace.html mathworld: Necklace], {{OEIS el|1=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 mw-collapsible mw-collapsed"
!colspan=5| A4 honeycombs
|-
![[:File:Symmetries_of_pentagon.png|Pentagon<BR>symmetry]]
![[Coxeter notation|Extended<BR>symmetry]]
!Extended<BR>diagram
!Extended<BR>group
!Honeycomb diagrams
|-
!a1
![3<sup>[5]</sup>]
!{{CDD|node|split1|nodes|3ab|branch}}
|<math>{\tilde{A}}_4</math>
| (None)
|-
!i2
!{{Brackets|3<sup>[5]</sup>}}
!{{CDD|node_c1|split1|nodeab_c2|3ab|branch_c3}}
| <math>{\tilde{A}}_4</math>×2
|{{CDD|node_1|split1|nodes|3ab|branch}}&nbsp;<sub>[[5-cell honeycomb|1]]</sub>,{{CDD|node|split1|nodes_11|3ab|branch}}&nbsp;<sub>[[Rectified 5-cell honeycomb|2]]</sub>,{{CDD|node|split1|nodes|3ab|branch_11}}&nbsp;<sub>[[Cyclotruncated 5-cell honeycomb|3]]</sub>,
{{CDD|node_1|split1|nodes_11|3ab|branch}}&nbsp;<sub>[[Truncated 5-cell honeycomb|4]]</sub>,{{CDD|node_1|split1|nodes|3ab|branch_11}}&nbsp;<sub>[[Cantellated 5-cell honeycomb|5]]</sub>,{{CDD|node|split1|nodes_11|3ab|branch_11}}&nbsp;<sub>[[Bitruncated 5-cell honeycomb|6]]</sub>
|-
!r10
![5[3<sup>[5]</sup>]]
!{{CDD|node_c1|split1|nodeab_c1|3ab|branch_c1}}
| <math>{\tilde{A}}_4</math>×10
|{{CDD|node_1|split1|nodes_11|3ab|branch_11}}&nbsp;<sub>[[Omnitruncated 5-cell honeycomb|7]]</sub>
|}<noinclude>

==References==
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