Apeirogon
In geometry, an apeirogon is a generalized polygon with a countably infinite number of sides. It can be considered as the limit of an n-sided polygon as n approaches infinity. The interior of a linear apeirogon can be defined by a direction order of vertices, and defining half the plane as the interior.
This article describes an apeirogon in its linear form as a tessellation or partition of a line.
Regular apeirogon
A regular apeirogon has equal edge lengths, just like any regular polygon, {p}. Its Schläfli symbol is {∞}, and its Coxeter-Dynkin diagram is 

. It is the first in the dimensional family of regular hypercubic honeycombs.
This line may be considered as a circle of infinite radius, by analogy with regular polygons with great number of edges, which resemble a circle.
In two dimensions, a regular apeirogon divides the plane into two half-planes as a regular apeirogonal dihedron. The interior of an apeirogon can be defined by its orientation, filling one half plane. Dually the apeirogonal hosohedron has digon faces and an apeirogonal vertex figure, {2, ∞}. A truncated apeirogonal hosohedron becomes a apeirogonal prism, with each vertex bounded by two squares and an apeirogon. An alternated apeirogonal prism is a apeirogonal antiprism, with each vertex bounded by three triangles and an apeirogon.