Point set registration

This honeycomb is one of seven unique uniform honeycombs constructed by the ${\tilde{A}}_4$ Coxeter group. The symmetry can be multiplied by the symmetry of rings in the Coxeter–Dynkin diagrams:

Pentagon symmetry	Extended symmetry	Extended diagram	Extended order	Honeycomb diagrams
a1	[3[5]]	Template:CDD	×1	(None)
i2	[[3[5]]]	Template:CDD	×2	Template:CDD 1,Template:CDD 2,Template:CDD 3, Template:CDD 4,Template:CDD 5,Template:CDD 6
r10	[5[3[5]]]	Template:CDD	×10	Template:CDD 7

References

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