Order-infinite-3 triangular honeycomb: Difference between revisions

Revision as of 08:18, 29 September 2017

Revision as of 08:19, 29 September 2017

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|bgcolor=#efdcc3|Edge figure||[[Apeirogon|{∞}]]

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|bgcolor=#efdcc3|Vertex figure||[[Infinite-order heptagonalapeirogonal tiling|{&infin;,∞}]] [[File:H2 tiling 2ii-4.png|40px]]<BR>{(&infin;,∞,&infin;)} [[File:H2 tiling iii-4.png|40px]]

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

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|bgcolor=#efdcc3|Properties||Regular

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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-infinite-infinite triangular honeycomb''' (or '''3,&infin;,∞ honeycomb''') is a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) with [[Schläfli symbol]] {3,&infin;,∞}. It has infinitely many [[infinite-order triangular tiling]], {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 ''infinite-order heptagonalapeirogonal tiling'', {&infin;,∞}, [[vertex figure]].

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=== Order-infinite-3 square honeycomb===

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