apeirogonal tiling
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.{{citation
| last1 = Mosseri | first1 = R.
| last2 = Sadoc | first2 = J.F.
| doi = 10.1051/jphyslet:01982004308024900
| issue = 8
| journal = Journal de Physique Lettres
| pages = 249–252
| title = The Bethe lattice: a regular tiling of the hyperbolic plane
| volume = 43
| year = 1982| url = https://hal.archives-ouvertes.fr/jpa-00232041/file/ajp-jphyslet_1982_43_8_249_0.pdf
}}