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...hyperbolic plane]], or some other two-dimensional space by [[apeirogon]]s. Tilings of this type include: *[[Order-2 apeirogonal tiling]], Euclidean tiling of two half-spaces ...

...of this honeycomb is a triangular tiling. Thus, infinitely many hexagonal tilings meet at each vertex of this honeycomb.<ref>Coxeter ''The Beauty of Geometry == Related tilings == ...

...[vertex figure]] of this honeycomb is a tetrahedron. Thus, four hexagonal tilings meet at each vertex of this honeycomb, six hexagons meet at each vertex, an ...] towards a single ideal point. It can be seen as similar to the [[order-3 apeirogonal tiling]], {&infin;,3} of H², with [[horocycle]]s circumscribing ...

...4,4}, it has four [[square tiling]]s around each edge, and infinite square tilings around each vertex in a [[square tiling]] [[vertex figure]].<ref>Coxeter '' ...DD|node_1|split1-44|nodes|split2-44|node}} with 3 types (colors) of square tilings in a ratio of 2:1:1. ...

...ode|6|node_g|3sg|node_g}}, which alternates 3 types (colors) of triangular tilings around every edge. In [[Coxeter notation]], the removal of the 3rd and 4th == Related Tilings == ...

...vertex figure]] of this honeycomb is an octahedron. Thus, eight hexagonal tilings meet at each vertex of this honeycomb, and the six edges meeting at each ve ...e.png|200px]]<BR>The honeycomb is analogous to the H² [[order-4 apeirogonal tiling]], {&infin;,4}, shown here with one green [[apeirogon]] outlined by ...

In [[geometry]], many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by [[Wythoff c ...e [[Euclidean plane]]. A few of the [[List of regular polytopes#Hyperbolic tilings|infinitely many]] such patterns in the [[Hyperbolic space|hyperbolic plane] ...

...[[vertex figure]] of this honeycomb is an icosahedron. Thus, 20 hexagonal tilings meet at each vertex of this honeycomb.<ref>Coxeter ''The Beauty of Geometry ...ng honeycomb is similar to the 2D hyperbolic regular paracompact [[order-5 apeirogonal tiling]], {&infin;,5}, with five [[apeirogon]]al faces meeting around every ...

..., it has three [[square tiling]]s, {4,4}, around each edge, and six square tilings around each vertex, in a [[cube|cubic]] {4,3} [[vertex figure]].<ref>Coxete ...}, and lastly a construction with three types (colors) of checkered square tilings {{CDD|node_1|4|node|4|node_g|3sg|node_g}} ↔ {{CDD|node|4|node_1|split1-44|n ...

...group]] but not a two-dimensional family of symmetries. There exist binary tilings with tiles of arbitrarily small area. ...|Károly Böröczky|hu|Böröczky Károly (matematikus, 1964)}}. Closely related tilings have been used since the late 1930s in the [[Smith chart]] for radio engine ...

...cle (geometry)|hypercycle]] surfaces, similar to the paracompact [[order-3 apeirogonal tiling]], {{CDD|node|3|node|infin|node_1}}: ...aapeirogonal tiling, r{4,∞}, {{CDD||node|4|node_1|infin|node}} alternating apeirogonal and square faces: ...

...of regular polytopes and compounds#Hyperbolic star-tilings|star hyperbolic tilings]] {p/2,p} ...to the <math>{\tilde{G}}_2</math>, [6,3] Coxeter group and relates uniform tilings as ringed diagrams. ...