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This characterization of the regular polygons naturally characterizes the regular apeirogons as well. The discrete apeirogons are the results of blending the 1-dimensional apeirogon with other polygons. [4]: 231 Since every polygon is a quotient of the apeirogon, the blend of any polygon with an apeirogon produces another apeirogon. [3]
Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions, although the regular forms trigon, tetragon, and enneagon are sometimes encountered as well.
The angled edges of an apeirogonal antiprism represent a regular zig-zag skew apeirogon.. A regular zig-zag skew apeirogon has (2*∞), D ∞d Frieze group symmetry.. Regular zig-zag skew apeirogons exist as Petrie polygons of the three regular tilings of the plane: {4,4}, {6,3}, and {3,6}.
Apeirogon; Tilings. List of uniform tilings; ... Hyperbolic triangle (non-Euclidean geometry) Isosceles triangle; Kepler triangle; Reuleaux triangle; Right triangle;
Special polygons in hyperbolic geometry are the regular apeirogon and pseudogon uniform polygons with an infinite number of sides. In Euclidean geometry , the only way to construct such a polygon is to make the side lengths tend to zero and the apeirogon is indistinguishable from a circle, or make the interior angles tend to 180° and the ...
Heptagram – star polygon with 7 sides; Octagram – star polygon with 8 sides Star of Lakshmi (example) Enneagram - star polygon with 9 sides; Decagram - star polygon with 10 sides; Hendecagram - star polygon with 11 sides; Dodecagram - star polygon with 12 sides; Apeirogon - generalized polygon with countably infinite set of sides
Some regular polygons are easy to construct with compass and straightedge; other regular polygons are not constructible at all. The ancient Greek mathematicians knew how to construct a regular polygon with 3, 4, or 5 sides, [11]: p. xi and they knew how to construct a regular polygon with double the number of sides of a given regular polygon.
Skew polygons must have at least four vertices. The interior surface and corresponding area measure of such a polygon is not uniquely defined. Skew infinite polygons (apeirogons) have vertices which are not all colinear. A zig-zag skew polygon or antiprismatic polygon [2] has vertices which alternate on two parallel planes, and thus must be ...