
260px|thumb|A partition of the Euclidean line into infinitely many equal-length segments can be understood as a regular apeirogon. In geometry, an apeirogon () or infinite polygon is a polygon with an infinite number of sides. Apeirogons are the rank 2 case of infinite polytopes. In some literature, the term "apeirogon" may refer only to the regular apeirogon, with an infinite dihedral group of symmetries.
via Wikipedia infobox
{{Infobox Polygon | name = Apeirogon (regular) | image = regular apeirogon.svg | edges = ∞ | schläfli = {∞} | coxeter = | angle = 180° | dual = Self-dual }} 260px|thumb|A partition of the Euclidean line into infinitely many equal-length segments can be understood as a regular apeirogon. In geometry, an apeirogon () or infinite polygon is a polygon with an infinite number of sides. Apeirogons are the rank 2 case of infinite polytopes. In some literature, the term "apeirogon" may refer only to the regular apeirogon, with an infinite dihedral group of symmetries.
==Definitions== ===Geometric apeirogon=== Given a point A0 in a Euclidean space and a translation S, define the point Ai to be the point obtained from i applications of the translation S to A0, so Ai = Si(A0). The set of vertices Ai with i any integer, together with edges connecting adjacent vertices, is a sequence of equal-length segments of a line, and is called the regular apeirogon as defined by H. S. M. Coxeter.
Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).