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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-7-3 square honeycomb''' (or '''4,7,3 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-7-3 square honeycomb'' is {4,7,3}, with three order-4 heptagonal tilings meeting at each edge. The [[vertex figure]] of this honeycomb is a heptagonal tiling, {7,3}.
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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-7-3 pentagonal honeycomb''' (or '''5,7,3 honeycomb''') a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]). Each infinite cell consists of an [[order-7 pentagonal 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-6-3 pentagonal honeycomb'' is {5,7,3}, with three ''order-7 pentagonal tilings'' meeting at each edge. The [[vertex figure]] of this honeycomb is a heptagonal tiling, {7,3}.
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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-7-3 hexagonal honeycomb''' (or '''6,7,3 honeycomb''') a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]). Each infinite cell consists of a [[order-6 hexagonal 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-7-3 hexagonal honeycomb'' is {6,7,3}, with three order-5 hexagonal tilings meeting at each edge. The [[vertex figure]] of this honeycomb is a heptagonal tiling, {7,3}.
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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-7-3 apeirogonal honeycomb''' (or '''∞,7,3 honeycomb''') a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]). Each infinite cell consists of an [[order-7 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 {∞,7,3}, with three ''order-7 apeirogonal tilings'' meeting at each edge. The [[vertex figure]] of this honeycomb is a heptagonal tiling, {7,3}.
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