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-
apeirogonal tiling form a Bethe lattice, a regular infinite tree.
See also
*Apeirogonal antiprism
*Apeirogonal prism
*Apeirohedron
References
{{set index article, mathematics
Apeirogonal tilings