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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.
A regular triangle, octagon, and icositetragon can completely fill a plane vertex. An icositetragram is a 24-sided star polygon. There are 3 regular forms given by Schläfli symbols: {24/5}, {24/7}, and {24/11}. There are also 7 regular star figures using the same vertex arrangement: 2{12}, 3{8}, 4{6}, 6{4}, 8{3}, 3{8/3}, and 2{12/5}.
A regular digon has both angles equal and both sides equal and is represented by Schläfli symbol {2}. It may be constructed on a sphere as a pair of 180 degree arcs connecting antipodal points, when it forms a lune. The digon is the simplest abstract polytope of rank 2. A truncated digon, t{2} is a square, {4}. An alternated digon, h{2} is a ...
In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star .
Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into m(m-1)/2 parallelograms. [ 4 ] In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi.
Any polygon has as many corners as it has sides. Each corner has several angles. The two most important ones are: Interior angle – The sum of the interior angles of a simple n-gon is (n − 2) × π radians or (n − 2) × 180 degrees. This is because any simple n-gon ( having n sides ) can be considered to be made up of (n − 2) triangles ...
Given a point A 0 in a Euclidean space and a translation S, define the point A i to be the point obtained from i applications of the translation S to A 0, so A i = S i (A 0).The set of vertices A i 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.
Regular triacontagon with given circumcircle. D is the midpoint of AM, DC = DF, and CF, which is the side length of the regular pentagon, is E 25 E 1.Since 1/30 = 1/5 - 1/6, the difference between the arcs subtended by the sides of a regular pentagon and hexagon (E 25 E 1 and E 25 A) is that of the regular triacontagon, AE 1.