This honeycomb is one of 45 unique uniform honeycombs[1] constructed by the 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]]

i2 [[3[9]]] ×2

1 2

i6 [3[3[9]]] ×6
r18 [9[3[9]]] ×18 3

References

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