This honeycomb is one of 77 uniform honeycombs constructed by the <math>{\tilde{D}}_7</math> Coxeter group, all but 10 repeated in other families by extended symmetry, seen in the graph symmetry of rings in the Coxeter–Dynkin diagrams. The 77 permutations are listed with its highest extended symmetry, and related <math>{\tilde{B}}_7</math> and <math>{\tilde{C}}_7</math> constructions:
| D7 honeycombs
|
Extended symmetry
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Extended diagram
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Order
|
Honeycombs
|
| [31,1,3,3,3,31,1]
|
File:CDel nodes.pngFile:CDel split2.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes.png
|
×1
|
File:CDel nodes 10ru.pngFile:CDel split2.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 10lu.png, File:CDel nodes 10ru.pngFile:CDel split2.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 10lu.png, File:CDel nodes 10ru.pngFile:CDel split2.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 10lu.png, File:CDel nodes 10ru.pngFile:CDel split2.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 10lu.png, File:CDel nodes 10ru.pngFile:CDel split2.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 10lu.png, File:CDel nodes 10ru.pngFile:CDel split2.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes 10lu.png,
|
| [[31,1,3,3,3,31,1]]
|
File:CDel nodeab c1-2.pngFile:CDel split2.pngFile:CDel node c3.pngFile:CDel 3.pngFile:CDel node c4.pngFile:CDel 3.pngFile:CDel node c4.pngFile:CDel 3.pngFile:CDel node c3.pngFile:CDel split1.pngFile:CDel nodeab c1-2.png
|
×2
|
File:CDel nodes 10ru.pngFile:CDel split2.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 10lu.png, File:CDel nodes 10ru.pngFile:CDel split2.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes 10lu.png, File:CDel nodes 10ru.pngFile:CDel split2.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 10lu.png, File:CDel nodes 10ru.pngFile:CDel split2.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes 10lu.png
|
<[31,1,3,3,3,31,1]> ↔ [31,1,3,3,3,3,4]
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File:CDel nodeab c1-2.pngFile:CDel split2.pngFile:CDel node c3.pngFile:CDel 3.pngFile:CDel node c4.pngFile:CDel 3.pngFile:CDel node c5.pngFile:CDel 3.pngFile:CDel node c6.pngFile:CDel split1.pngFile:CDel nodeab c7.png ↔ File:CDel nodeab c1-2.pngFile:CDel split2.pngFile:CDel node c3.pngFile:CDel 3.pngFile:CDel node c4.pngFile:CDel 3.pngFile:CDel node c5.pngFile:CDel 3.pngFile:CDel node c6.pngFile:CDel 3.pngFile:CDel node c7.pngFile:CDel 4.pngFile:CDel node.png
|
×2
|
...
|
<<[31,1,3,3,3,31,1]>> ↔ [4,3,3,3,3,3,4]
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File:CDel nodeab c1.pngFile:CDel split2.pngFile:CDel node c2.pngFile:CDel 3.pngFile:CDel node c3.pngFile:CDel 3.pngFile:CDel node c4.pngFile:CDel 3.pngFile:CDel node c5.pngFile:CDel split1.pngFile:CDel nodeab c6.png ↔ File:CDel node.pngFile:CDel 4.pngFile:CDel node c1.pngFile:CDel 3.pngFile:CDel node c2.pngFile:CDel 3.pngFile:CDel node c3.pngFile:CDel 3.pngFile:CDel node c4.pngFile:CDel 3.pngFile:CDel node c5.pngFile:CDel 3.pngFile:CDel node c6.pngFile:CDel 4.pngFile:CDel node.png
|
×4
|
...
|
[<<[31,1,3,3,3,31,1]>>] ↔ [[4,3,3,3,3,3,4]]
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File:CDel nodeab c1.pngFile:CDel split2.pngFile:CDel node c2.pngFile:CDel 3.pngFile:CDel node c3.pngFile:CDel 3.pngFile:CDel node c3.pngFile:CDel 3.pngFile:CDel node c2.pngFile:CDel split1.pngFile:CDel nodeab c1.png ↔ File:CDel node.pngFile:CDel 4.pngFile:CDel node c1.pngFile:CDel 3.pngFile:CDel node c2.pngFile:CDel 3.pngFile:CDel node c3.pngFile:CDel 3.pngFile:CDel node c3.pngFile:CDel 3.pngFile:CDel node c2.pngFile:CDel 3.pngFile:CDel node c1.pngFile:CDel 4.pngFile:CDel node.png
|
×8
|
...
|
References