Order-infinite-3 triangular honeycomb: Difference between revisions

Revision as of 03:18, 28 September 2017

Revision as of 03:19, 28 September 2017

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|bgcolor=#efdcc3|Edge figure||[[square|{4}]]

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|bgcolor=#efdcc3|Vertex figure||[[Order-4 hexagonalapeirogonal tiling|{&infin;,4}]] [[File:H2 tiling 24i-1.png|50px]]<BR>r{&infin;,&infin;} [[File:H2_tiling_2ii-2.png|50px]]

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|bgcolor=#efdcc3|Dual||[[Order-infinite-3 square honeycomb|{4,&infin;,3}]]

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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-infinite-4 triangular honeycomb''' (or '''3,&infin;,4 honeycomb''') is a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) with [[Schläfli symbol]] {3,&infin;,4}.

It has four [[Infinite-order triangular tiling]]s, {3,&infin;}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many Infinite-order triangular tilings existing around each vertex in an [[order-4 hexagonalapeirogonal tiling]] [[vertex arrangement]].

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