Difference between revisions of "Template:A8 honeycombs"

Revision as of 16:38, 20 February 2016

This honeycomb is one of 45 unique uniform honeycombs^[1] constructed by the <math>{\tilde{A}}_8</math> Coxeter group. The symmetry can be multiplied by the ring symmetry of the Coxeter diagrams:

A8 honeycombs
Enneagon symmetry	Symmetry	Extended diagram	Extended group	Honeycombs
a1	[3^[9]]	File:CDel node.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch.png	<math>{\tilde{A}}_8</math>	File:CDel node 1.png File:CDel split1.png File:CDel nodes 10lur.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 10lr.png File:CDel 3ab.png File:CDel branch.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 10lur.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch 10l.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch 10l.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 10lr.png File:CDel 3ab.png File:CDel branch.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch 10l.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 10lur.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 10lr.png File:CDel 3ab.png File:CDel branch 01l.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 10lur.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch 10l.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 10lr.png File:CDel 3ab.png File:CDel branch 01l.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 10lr.png File:CDel 3ab.png File:CDel branch 10l.png File:CDel node.png File:CDel split1.png File:CDel nodes 10lur.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch 10l.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 10lur.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch 10l.png
i2	[[3^[9]]]	File:CDel node c1.png File:CDel split1.png File:CDel nodeab c2.png File:CDel 3ab.png File:CDel nodeab c3.png File:CDel 3ab.png File:CDel nodeab c4.png File:CDel 3ab.png File:CDel branch c5.png	<math>{\tilde{A}}_8</math>×2	File:CDel node 1.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch.png₁ File:CDel node.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch.png File:CDel node.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch.png File:CDel node.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch 11.png ₂ File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch.png File:CDel node.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch 11.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch 11.png
i6	[3[3^[9]]]	File:CDel node c3.png File:CDel split1.png File:CDel nodeab c1.png File:CDel 3ab.png File:CDel nodeab c1.png File:CDel 3ab.png File:CDel nodeab c3.png File:CDel 3ab.png File:CDel branch c1.png	<math>{\tilde{A}}_8</math>×6	File:CDel node 1.png File:CDel split1.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes.png File:CDel 3ab.png File:CDel branch 11.png
r18	[9[3^[9]]]	File:CDel node c1.png File:CDel split1.png File:CDel nodeab c1.png File:CDel 3ab.png File:CDel nodeab c1.png File:CDel 3ab.png File:CDel nodeab c1.png File:CDel 3ab.png File:CDel branch c1.png	<math>{\tilde{A}}_8</math>×18	File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel 3ab.png File:CDel branch 11.png ₃

References

↑ * Weisstein, Eric W. "Necklace". MathWorld., A000029 46-1 cases, skipping one with zero marks

[1] * Weisstein, Eric W. "Necklace". MathWorld., A000029 46-1 cases, skipping one with zero marks

[1]

@@ Line 2: / Line 2: @@
 the <math>{\tilde{A}}_8</math> [[Coxeter group]]. The symmetry can be multiplied by the ring symmetry of the [[Coxeter diagram]]s:
 {| class="wikitable collapsible collapsed"
-!colspan=4|A8 honeycombs
+!colspan=5|A8 honeycombs
 |-
 ![[:File:Regular_enneagon_symmetries.png|Enneagon<BR>symmetry]]

Difference between revisions of "Template:A8 honeycombs"

Revision as of 16:38, 20 February 2016

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