Order-infinite-3 triangular honeycomb: Difference between revisions

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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-infinite-4 triangular honeycomb''' (or '''3,∞,4 honeycomb''') is a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) with [[Schläfli symbol]] {3,∞,4}.
 
It has four [[Infinite-order triangular tiling]]s, {3,∞}, 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 apeirogonal tiling]] [[vertex arrangementfigure]].
 
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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-infinite-6 hexagonal honeycomb''' (or '''6,∞,6 honeycomb''') is a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) with [[Schläfli symbol]] {6,∞,6}. It has six [[infinite-order hexagonal tiling]]s, {6,∞}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many hexagonal tilings existing around each vertex in an [[order-6 apeirogonal tiling]] [[vertex arrangementfigure]].
 
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In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-infinite-7 heptagonal honeycomb''' (or '''7,∞,7 honeycomb''') is a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) with [[Schläfli symbol]] {7,∞,7}. It has seven [[infinite-order heptagonal tiling]]s, {7,∞}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many heptagonal tilings existing around each vertex in an [[order-7 heptagonal tiling]] [[vertex arrangementfigure]].
 
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