Concept
Order-2 apeirogonal tiling
Related concepts (4)
Apeirogonal antiprism
In geometry, an apeirogonal antiprism or infinite antiprism is the arithmetic limit of the family of antiprisms; it can be considered an infinite polyhedron or a tiling of the plane. If the sides are equilateral triangles, it is a uniform tiling. In general, it can have two sets of alternating congruent isosceles triangles, surrounded by two half-planes. The apeirogonal antiprism is the arithmetic limit of the family of antiprisms sr{2, p} or p.3.3.3, as p tends to infinity, thereby turning the antiprism into a Euclidean tiling.
Apeirogonal prism
In geometry, an apeirogonal prism or infinite prism is the arithmetic limit of the family of prisms; it can be considered an infinite polyhedron or a tiling of the plane. Thorold Gosset called it a 2-dimensional semi-check, like a single row of a checkerboard. If the sides are squares, it is a uniform tiling. If colored with two sets of alternating squares it is still uniform. File:Infinite prism alternating.svg|Uniform variant with alternate colored square faces. File:Infinite_bipyramid.
Apeirogon
In geometry, an apeirogon () or infinite polygon is a polygon with an infinite number of sides. Apeirogons are the two-dimensional case of infinite polytopes. In some literature, the term "apeirogon" may refer only to the regular apeirogon, with an infinite dihedral group of symmetries. 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).
Uniform polyhedron
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent. Uniform polyhedra may be regular (if also face- and edge-transitive), quasi-regular (if also edge-transitive but not face-transitive), or semi-regular (if neither edge- nor face-transitive). The faces and vertices need not be convex, so many of the uniform polyhedra are also star polyhedra.