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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.
1.1 Polygons with specific numbers of sides. ... This is a list of two-dimensional geometric shapes in Euclidean and other geometries. ... Regular polygon; Simple ...
A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples.
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.
The regular finite polygons in 3 dimensions are exactly the blends of the planar polygons (dimension 2) with the digon (dimension 1). They have vertices corresponding to a prism ({n/m}#{} where n is odd) or an antiprism ({n/m}#{} where n is even). All polygons in 3 space have an even number of vertices and edges.
Polygonal numbers: These are numbers that can be represented as dots that are arranged in the shape of a regular polygon, including Triangular numbers, Square numbers, Pentagonal numbers, Hexagonal numbers, Heptagonal numbers, Octagonal numbers, Nonagonal numbers, Decagonal numbers, Hendecagonal numbers, and Dodecagonal numbers.
A new figure is obtained by rotating these regular n/m-gons one vertex to the left on the original polygon until the number of vertices rotated equals n/m minus one, and combining these figures. An extreme case of this is where n/m is 2, producing a figure consisting of n/2 straight line segments; this is called a degenerate star polygon.
In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon [1]: 2-3 . These are one type of 2-dimensional figurate numbers . Polygonal numbers were first studied during the 6th century BC by the Ancient Greeks, who investigated and discussed properties of oblong , triangular , and square numbers ...