In geometry, an apeirogonal tiling is a tessellation of the Euclidean plane, hyperbolic plane, or some other two-dimensional space by apeirogons. Tilings of this type include:
Order-2 apeirogonal tiling, Euclidean tiling of two half-spaces Order-3 apeirogonal tiling, hyperbolic tiling with 3 apeirogons around a vertex Order-4 apeirogonal tiling, hyperbolic tiling with 4 apeirogons around a vertex Order-5 apeirogonal tiling, hyperbolic tiling with 5 apeirogons around a vertex Infinite-order apeirogonal tiling, hyperbolic tiling with an infinite number of apeirogons around a vertex The vertices of an order- k {\displaystyle k} apeirogonal tiling form a Bethe lattice, a regular infinite tree.
See also Apeirogonal antiprism Apeirogonal prism Apeirohedron
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