Template:A6 honeycombs

This honeycomb is one of 17 unique uniform honeycombs^[1] constructed by the ${\tilde {A}}_{6}$ Coxeter group, grouped by their extended symmetry of the Coxeter–Dynkin diagrams:

A6 honeycombs
Heptagon symmetry	Extended symmetry	Extended diagram	Extended group	Honeycombs
a1	[3^[7]]	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 branch.png	${\tilde {A}}_{6}$	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 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 branch 10l.png
i2	[[3^[7]]]	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 branch c4.png	${\tilde {A}}_{6}$ ×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 branch.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 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 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 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 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 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 branch 11.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 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 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 branch 11.png₂ 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 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 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 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 branch 11.png
r14	[7[3^[7]]]	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 branch c1.png	${\tilde {A}}_{6}$ ×14	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 branch 11.png₃

References

↑ * Weisstein, Eric W. "Necklace". MathWorld., OEIS sequence A000029 18-1 cases, skipping one with zero marks

[1] * Weisstein, Eric W. "Necklace". MathWorld., OEIS sequence A000029 18-1 cases, skipping one with zero marks

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