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The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals times the apothem (radius of the inscribed circle). All internal angles are 120 degrees . A regular hexagon has six rotational symmetries ( rotational symmetry of order six ) and six reflection symmetries ( six lines of symmetry ), making ...
A pentagon is a five-sided polygon. A regular pentagon has 5 equal edges and 5 equal angles. In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain.
A hexagram or sexagram is a six-pointed geometric star figure with the Schläfli symbol {6/2}, 2{3}, or {{3}}. The term is used to refer to a compound figure of two equilateral triangles. The intersection is a regular hexagon. The hexagram is part of an infinite series of shapes which are compounds of two n-dimensional simplices.
As n approaches infinity, the internal angle approaches 180 degrees. For a regular polygon with 10,000 sides (a myriagon) the internal angle is 179.964°. As the number of sides increases, the internal angle can come very close to 180°, and the shape of the polygon approaches that of a circle. However the polygon can never become a circle.
A regular icositrigon has internal angles of degrees, with an area of = = , where is side length and is the inradius, or apothem. The regular icositrigon is not constructible with a compass and straightedge or angle trisection , [ 1 ] on account of the number 23 being neither a Fermat nor Pierpont prime .
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}.
A skew polygon has equal angles off a plane, like this skew octagon alternating red and blue edges on a cube. Direct Indirect Counter-turned A multi-turning equiangular polygon can be direct, like this octagon, <8/2>, has 8 90° turns, totaling 720°. A concave indirect equiangular polygon, <5-2>, counterclockwise has 4 left turns and one right ...
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.