Template:A7 honeycombs

This honeycomb is one of 29 unique uniform honeycombs^[1] constructed by the ${\tilde {A}}_{7}$ Coxeter group, grouped by their extended symmetry of rings within the regular octagon diagram:

A7 honeycombs
Octagon symmetry	Extended symmetry	Extended diagram	Extended group	Honeycombs
a1File:Octagon symmetry a1.png	[3^[8]]	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 split2.png File:CDel node.png	${\tilde {A}}_{7}$	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 10lru.png File:CDel split2.png File:CDel node.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 split2.png File:CDel node 1.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 10lur.png File:CDel 3ab.png File:CDel nodes 10lr.png File:CDel 3ab.png File:CDel nodes.png File:CDel split2.png File:CDel node 1.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 split2.png File:CDel node.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 10lur.png File:CDel 3ab.png File:CDel nodes 10lr.png File:CDel 3ab.png File:CDel nodes 11.png File:CDel split2.png File:CDel node.png
d2File:Octagon symmetry d2.png	<[3^[8]]>	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 split2.png File:CDel node c5.png	${\tilde {A}}_{7}$ ×2₁	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 split2.png File:CDel node.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 split2.png File:CDel node.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 split2.png File:CDel node.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 split2.png File:CDel node.png₁ 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 split2.png File:CDel node.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 split2.png File:CDel node.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 split2.png File:CDel node.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 split2.png File:CDel node.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 split2.png File:CDel node.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 split2.png File:CDel node.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 split2.png File:CDel node.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 split2.png File:CDel node 1.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 split2.png File:CDel node 1.png
p2File:Octagon symmetry p2.png	[[3^[8]]]	File:CDel branch c1.png File:CDel 3ab.png File:CDel nodeab c2.png File:CDel 3ab.png File:CDel nodeab c3.png File:CDel 3ab.png File:CDel branch c4.png	${\tilde {A}}_{7}$ ×2₂	File:CDel branch 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 ₂ File:CDel branch.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 branch 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 branch 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 branch 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 branch 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
d4File:Octagon symmetry d4.png	<2[3^[8]]>	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 c2.png File:CDel split2.png File:CDel node c1.png	${\tilde {A}}_{7}$ ×4₁	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 split2.png File:CDel node 1.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 split2.png File:CDel node.png
p4File:Octagon symmetry p4.png	[2[3^[8]]]	File:CDel branch c1.png File:CDel 3ab.png File:CDel nodeab c2.png File:CDel 3ab.png File:CDel nodeab c2.png File:CDel 3ab.png File:CDel branch c1.png	${\tilde {A}}_{7}$ ×4₂	File:CDel branch 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
d8File:Octagon symmetry d8.png	[4[3^[8]]]	File:CDel node c1.png File:CDel split1.png File:CDel nodeab c2.png File:CDel 3ab.png File:CDel nodeab c1.png File:CDel 3ab.png File:CDel nodeab c2.png File:CDel split2.png File:CDel node c1.png	${\tilde {A}}_{7}$ ×8	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 split2.png File:CDel node 1.png
r16File:Octagon symmetry r16.png	[8[3^[8]]]	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 split2.png File:CDel node c1.png	${\tilde {A}}_{7}$ ×16	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 split2.png File:CDel node 1.png₃

References

↑ Weisstein, Eric W. "Necklace". MathWorld., OEIS sequence A000029 30-1 cases, skipping one with zero marks

[1] Weisstein, Eric W. "Necklace". MathWorld., OEIS sequence A000029 30-1 cases, skipping one with zero marks

[1]

Anonymous

Search

Template:A7 honeycombs

Namespaces

More

Page actions

References

Navigation

Navigation

Wiki tools

Wiki tools

Anonymous

Search

Template:A7 honeycombs

References

Navigation

Wiki tools

Page tools

Other projects

Categories