Order-infinite-3 triangular honeycomb: Difference between revisions

Revision as of 01:28, 28 September 2017

Revision as of 01:28, 28 September 2017

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=== Order-infinityinfinite-3 apeirogonal honeycomb===

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!bgcolor=#efdcc3 colspan=2|Order-infinityinfinite-3 apeirogonal honeycomb

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|bgcolor=#efdcc3|Type||[[List of regular polytopes#Tessellations of hyperbolic 3-space|Regular honeycomb]]

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|bgcolor=#efdcc3|Properties||Regular

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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''Order-infinityinfinite-3 apeirogonal honeycomb''' (or '''∞,∞,3 honeycomb''') a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]). Each infinite cell consists of an [[infinite-order apeirogonal tiling]] whose vertices lie on a [[Hypercycle (geometry)|2-hypercycle]], each of which has a limiting circle on the ideal sphere.

The [[Schläfli symbol]] of the apeirogonal tiling honeycomb is {∞,∞,3}, with three ''infinite-order apeirogonal tilings'' meeting at each edge. The [[vertex figure]] of this honeycomb is a heptagonal tiling, {∞,3}.