geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, 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

See also