Template:D5 honeycombs

This honeycomb is one of 20 uniform honeycombs constructed by the <math>{\tilde{D}}_5</math> Coxeter group, all but 3 repeated in other families by extended symmetry, seen in the graph symmetry of rings in the Coxeter–Dynkin diagrams. The 20 permutations are listed with its highest extended symmetry relation:

D5 honeycombs
Extended symmetry	Extended diagram	Extended group	Honeycombs
[3^1,1,3,3^1,1]	File:CDel nodes.png File:CDel split2.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes.png	<math>{\tilde{D}}_5</math>	File:CDel nodes 10ru.png File:CDel split2.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes 10lu.png
<[3^1,1,3,3^1,1]> ↔ [3^1,1,3,3,4]	File:CDel nodeab c1-2.png File:CDel split2.png File:CDel node c3.png File:CDel 3.png File:CDel node c4.png File:CDel split1.png File:CDel nodeab c5.png ↔ File:CDel nodeab c1-2.png File:CDel split2.png File:CDel node c3.png File:CDel 3.png File:CDel node c4.png File:CDel 3.png File:CDel node c5.png File:CDel 4.png File:CDel node.png	<math>{\tilde{D}}_5</math>×2₁ = <math>{\tilde{B}}_5</math>	File:CDel nodes 10ru.png File:CDel split2.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png, File:CDel nodes 10ru.png File:CDel split2.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png, File:CDel nodes 10ru.png File:CDel split2.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes.png, File:CDel nodes 10ru.png File:CDel split2.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes.png File:CDel nodes 10ru.png File:CDel split2.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png, File:CDel nodes 10ru.png File:CDel split2.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png, File:CDel nodes 10ru.png File:CDel split2.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png, File:CDel nodes 10ru.png File:CDel split2.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png
[[3^1,1,3,3^1,1]]	File:CDel nodeab c1-2.png File:CDel split2.png File:CDel node c3.png File:CDel 3.png File:CDel node c3.png File:CDel split1.png File:CDel nodeab c1-2.png	<math>{\tilde{D}}_5</math>×2₂	File:CDel nodes 10ru.png File:CDel split2.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes 10lu.png, File:CDel nodes 10ru.png File:CDel split2.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 10lu.png
<2[3^1,1,3,3^1,1]> ↔ [4,3,3,3,4]	File:CDel nodeab c1.png File:CDel split2.png File:CDel node c3.png File:CDel 3.png File:CDel node c2.png File:CDel split1.png File:CDel nodeab c4.png ↔ File:CDel node.png File:CDel 4.png File:CDel node c1.png File:CDel 3.png File:CDel node c3.png File:CDel 3.png File:CDel node c2.png File:CDel 3.png File:CDel node c4.png File:CDel 4.png File:CDel node.png	<math>{\tilde{D}}_5</math>×4₁ = <math>{\tilde{C}}_5</math>	File:CDel nodes 11.png File:CDel split2.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes.png, File:CDel nodes.png File:CDel split2.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes.png, File:CDel nodes 11.png File:CDel split2.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes.png, File:CDel nodes 11.png File:CDel split2.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png, File:CDel nodes 11.png File:CDel split2.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png, File:CDel nodes 11.png File:CDel split2.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png
[<2[3^1,1,3,3^1,1]>] ↔ [[4,3,3,3,4]]	File:CDel nodeab c1.png File:CDel split2.png File:CDel node c2.png File:CDel 3.png File:CDel node c2.png File:CDel split1.png File:CDel nodeab c1.png ↔ File:CDel node.png File:CDel 4.png File:CDel node c1.png File:CDel 3.png File:CDel node c2.png File:CDel 3.png File:CDel node c2.png File:CDel 3.png File:CDel node c1.png File:CDel 4.png File:CDel node.png	<math>{\tilde{D}}_5</math>×8 = <math>{\tilde{C}}_5</math>×2	File:CDel nodes.png File:CDel split2.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png, File:CDel nodes 11.png File:CDel split2.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png, File:CDel nodes 11.png File:CDel split2.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png

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