Order-7-3 triangular honeycomb: Difference between revisions

Revision as of 18:33, 27 January 2019

Revision as of 08:17, 15 February 2019

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== Geometry==

It has three [[order-7 triangular tiling]] {3,7} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many triangular tilings existing around each vertex in ana [[heptagonal tiling]] [[vertex figure]].

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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}.

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

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