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In geometry, an apeirogon is a generalized polygon with a countably infinite number of sides.〔Coxeter, Regular polytopes, p.45〕 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, . Its Schläfli symbol is , and Coxeter-Dynkin diagram . 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, . 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. |t |sr |} The regular apeirogon can also be seen as linear sets within 4 of the regular, uniform tilings, and 5 of the uniform dual tilings in the Euclidean plane. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Apeirogon」の詳細全文を読む スポンサード リンク
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