Order-8-3 triangular honeycomb: Difference between revisions

Revision as of 23:52, 6 April 2019

Revision as of 11:14, 2 December 2019

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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-8-3 square honeycomb''' (or '''4,8,3 honeycomb''') a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]). Each infinite cell consists of aan [[octagonal 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-8-3 square honeycomb'' is {4,8,3}, with three order-4 octagonal tilings meeting at each edge. The [[vertex figure]] of this honeycomb is an octagonal tiling, {8,3}.

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The [[Schläfli symbol]] of the apeirogonal tiling honeycomb is {∞,8,3}, with three ''order-8 apeirogonal tilings'' meeting at each edge. The [[vertex figure]] of this honeycomb is an octagonal tiling, {8,3}.

The "ideal surface" projection below is a plane-at-infinity, in the Poincaré half-space model of H3. It shows aan [[Apollonian gasket]] pattern of circles inside a largest circle.

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