Order-infinite-3 triangular honeycomb: Difference between revisions

Revision as of 07:38, 28 September 2017

Revision as of 07:40, 28 September 2017

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|bgcolor=#efdcc3|Faces||[[Square|{4}]]

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

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|bgcolor=#efdcc3|Dual||[[Order-infinite-4 triangular honeycomb|{3,∞,4}]]

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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-infinite-3 square honeycomb''' (or '''4,∞,3 honeycomb''') a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]). Each infinite cell consists of a [[heptagonal 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 square honeycomb'' is {4,∞,3}, with three orderinfinite-4order heptagonalsquare tilings meeting at each edge. The [[vertex figure]] of this honeycomb is aan order-3 heptagonalapeirogonal tiling, {∞,3}.

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