Template:A5 honeycombs

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This honeycomb is one of 12 unique uniform honeycombs[1] constructed by the <math>{\tilde{A}}_5</math> Coxeter group. The extended symmetry of the hexagonal diagram of the <math>{\tilde{A}}_5</math> Coxeter group allows for automorphisms that map diagram nodes (mirrors) on to each other. So the various 12 honeycombs represent higher symmetries based on the ring arrangement symmetry in the diagrams:

References

  1. mathworld: Necklace, Template:OEIS el 13-1 cases, skipping one with zero marks