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|bgcolor=#efdcc3|Faces||[[Apeirogon]] {∞}
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|bgcolor=#efdcc3|[[Vertex figure]]||[[infinite-order apeirogonal tiling|{∞,3}]]
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|bgcolor=#efdcc3|Dual||[[Order-infinite-infinite triangular honeycomb|{3,∞,∞}]]
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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-infinite-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 an infinite-order apeirogonal tiling, {∞,3}.
The "ideal surface" projection below is a plane-at-infinity, in the Poincare half-space model of H3. It shows a [[Apollonian gasket]] pattern of circles inside a largest circle.
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