Order-infinite-3 triangular honeycomb: Difference between revisions

Revision as of 07:40, 28 September 2017

Revision as of 07:41, 28 September 2017

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|bgcolor=#efdcc3|Faces||[[Hexagon|{6}]]

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|bgcolor=#efdcc3|[[Vertex figure]]||[[heptagonalorder-3 apeirogonal tiling|{∞,3}]]

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|bgcolor=#efdcc3|Dual||[[Order-infinite-6 triangular honeycomb|{3,∞,6}]]

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|bgcolor=#efdcc3|Properties||Regular

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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-infinite-3 hexagonal honeycomb''' (or '''6,∞,3 honeycomb''') a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]). Each infinite cell consists of a [[order-63 hexagonalapeirogonal 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 ''order-infinite-3 hexagonal honeycomb'' is {6,∞,3}, with three orderinfinite-5order hexagonal tilings meeting at each edge. The [[vertex figure]] of this honeycomb is a heptagonalorder-3 apeirogonal tiling, {∞,3}.

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