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Polygon - Taxonomic classification

Polygon - Taxonomic classification: Encyclopedia II - Polygon - Taxonomic classification

The taxonomic classification of polygons is illustrated by the following graph: Polygon / \ Simple Complex / \ / Convex Concave / / \ / / Cyclic Equilateral \ / Regular A polygon is called simple if ...

Polygon: Encyclopedia II - Polygon - Taxonomic classification

Polygon - Taxonomic classification

The taxonomic classification of polygons is illustrated by the following graph:

                                      Polygon
                                     /       \
                                 Simple     Complex
                                /      \      /
                           Convex    Concave /
                            /    \     /    /
                       Cyclic    Equilateral
                           \     /    
                           Regular

A polygon is called simple if it is described by a single, non-intersecting boundary (hence has an inside and an outside); otherwise it is called complex.
A simple polygon is called convex if it has no internal angles greater than 180°; otherwise it is called concave.
A simple polygon is called equilateral if all edges are of the same length. (A 5 or more sided polygon can be concave and equilateral)
A convex polygon is called concyclic or a cyclic polygon if all the vertices lie on a single circle.
A cyclic and equilateral polygon is called regular; for each number of sides, all regular polygons with the same number of sides are similar.
A complex polygon may also be defined as regular if it is cyclic and equilateral. These are called star polygons.

The regular polygons most commonly found include:

Equilateral triangle
Square
Regular pentagon
Regular hexagon
Regular octagon

Somewhat less common are:

Regular decagon
Regular dodecagon

See also: tilings of regular polygons

Other related archives

Bolyai-Gerwien theorem, Cyclic polygon, Euclidean geometry, Fermat primes, Gauss, Geometric shape, Greek, Green's theorem, MathWorld, Pick's theorem, Point in polygon, Polyform, Polygons, Polyhedron, Polytope, Simple polygon, Square, Star polygon, Synthetic geometry, Tiling, Tiling puzzle, angles, area, boundary, cartesian coordinates, circle, circumcircle, closed, complex, computational geometry, computer graphics, concave, constructible polygon, convex, cyclic polygon, decagon, degrees of freedom, dodecagon, equilateral, hexagon, iff, line segments, mathematicians, numeral, numerical prefix, octagon, odd, orbit (dynamics), pentagon, pentagram, planar, prime, quadrilateral, radians, rectangle, rhombus, ruler and compass, shape, similar, simple, star polygons, tilings of regular polygons, triangle, turns, winding number, π

Adapted from the Wikipedia article "Taxonomic classification", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki

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