Difference between revisions of "Template:D7 honeycombs"

Revision as of 03:08, 27 January 2016

This honeycomb is one of 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 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 20: / Line 20: @@
 !{{CDD|nodeab_c1-2|split2|node_c3|3|node_c4|3|node_c5|3|node_c6|split1|nodeab_c7}}<BR>= {{CDD|nodeab_c1-2|split2|node_c3|3|node_c4|3|node_c5|3|node_c6|3|node_c7|4|node}}
 ! ×2
-|
+| ...
 |- style="text-align:center;"
 !<<[3<sup>1,1</sup>,3,3,3,3<sup>1,1</sup>]>><BR>= [4,3,3,3,3,3,4]
 !{{CDD|nodeab_c1|split2|node_c2|3|node_c3|3|node_c4|3|node_c5|split1|nodeab_c6}}<BR>= {{CDD|node|4|node_c1|3|node_c2|3|node_c3|3|node_c4|3|node_c5|3|node_c6|4|node}}
 ! ×4
-|
+| ...
 |- style="text-align:center;"
 ![<<[3<sup>1,1</sup>,3,3,3,3<sup>1,1</sup>]>>]<BR>= [<span/>[4,3,3,3,3,3,4]]
 !{{CDD|nodeab_c1|split2|node_c2|3|node_c3|3|node_c3|3|node_c2|split1|nodeab_c1}}<BR>= {{CDD|node|4|node_c1|3|node_c2|3|node_c3|3|node_c3|3|node_c2|3|node_c1|4|node}}
 ! ×8
-|
+| ...
 |}{{Hidden end}}<noinclude>

Difference between revisions of "Template:D7 honeycombs"

Revision as of 03:08, 27 January 2016

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