Difference between revisions of "Template:D7 honeycombs"

Revision as of 23:41, 30 May 2017

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	Extended diagram	Order	Honeycombs
[3^1,1,3,3,3,3^1,1]	File:CDel nodes.png File:CDel split2.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes.png	×1	File:CDel nodes 10ru.png File:CDel split2.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 3.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.png File:CDel 3.png File:CDel node 1.png File:CDel 3.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 3.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.png File:CDel 3.png File:CDel node 1.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 3.png File:CDel node 1.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 3.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 10lu.png,
[[3^1,1,3,3,3,3^1,1]]	File:CDel nodeab c1-2.png File:CDel split2.png File:CDel node c3.png File:CDel 3.png File:CDel node c4.png File:CDel 3.png File:CDel node c4.png File:CDel 3.png File:CDel node c3.png File:CDel split1.png File:CDel nodeab c1-2.png	×2	File:CDel nodes 10ru.png File:CDel split2.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 3.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.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 10lu.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 3.png File:CDel node 1.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 3.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 10lu.png
<[3^1,1,3,3,3,3^1,1]> ↔ [3^1,1,3,3,3,3,4]	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 3.png File:CDel node c5.png File:CDel 3.png File:CDel node c6.png File:CDel split1.png File:CDel nodeab c7.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 3.png File:CDel node c6.png File:CDel 3.png File:CDel node c7.png File:CDel 4.png File:CDel node.png	×2	...
<<[3^1,1,3,3,3,3^1,1]>> ↔ [4,3,3,3,3,3,4]	File:CDel nodeab c1.png File:CDel split2.png File:CDel node c2.png File:CDel 3.png File:CDel node c3.png File:CDel 3.png File:CDel node c4.png File:CDel 3.png File:CDel node c5.png File:CDel split1.png File:CDel nodeab c6.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 c3.png File:CDel 3.png File:CDel node c4.png File:CDel 3.png File:CDel node c5.png File:CDel 3.png File:CDel node c6.png File:CDel 4.png File:CDel node.png	×4	...
[<<[3^1,1,3,3,3,3^1,1]>>] ↔ [[4,3,3,3,3,3,4]]	File:CDel nodeab c1.png File:CDel split2.png File:CDel node c2.png File:CDel 3.png File:CDel node c3.png File:CDel 3.png File:CDel node c3.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 c3.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 c1.png File:CDel 4.png File:CDel node.png	×8	...

References

@@ Line 1: / Line 1: @@
-This honeycomb is one of [[Uniform 8-polytope#Regular and uniform honeycombs|77 uniform honycombs]] 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 diagram]]s. The 77 permutations are listed with its highest extended symmetry, and related <math>{\tilde{B}}_7</math> and <math>{\tilde{C}}_7</math> constructions:
+This honeycomb is one of [[Uniform 8-polytope#Regular and uniform honeycombs|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 diagram]]s. The 77 permutations are listed with its highest extended symmetry, and related <math>{\tilde{B}}_7</math> and <math>{\tilde{C}}_7</math> constructions:
 {| class="wikitable collapsible collapsed"
 !colspan=4| D7 honeycombs

Difference between revisions of "Template:D7 honeycombs"

Revision as of 23:41, 30 May 2017

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