What is Regular polygon?
{{Regular polygon db|Regular polygon stat table|p17}} A '''regular polygon''' is a [[shape]] that can be drawn on a flat surface. It has [[Side|sides]] that are all the same [[length]], and its [[Angle|angles]] are all the same. In other words, a [[polygon]] which is both [[equilateral polygon|equilateral]] (which means all its sides have the same length) and [[equiangular polygon|equiangular]] (which means that all its angles are the same) is a regular polygon. It always has the same number of edges and [[Vertex|points]]. A polygon is also [[Convex set|convex]] if there aren't any two points within it that can't be connected with a straight line, where the entire straight line is also in it. An example of a concave shape is a five-pointed [[Star polygon|star]]. It's concave because you can connect two of the points of a star with a straight line, and most of the straight line doesn't go through the star. If a five-pointed star is both equilateral and equiangular, it is also a regular polygon, but it isn't a convex one. All regular concave polygons are stars. ==Examples== The simplest examples of regular convex polygons are: <gallery> Equilateral Triangle.svg|[[equilateral triangle]] Square diagonals.svg|[[square]] 01-Fünfeck simple.svg|[[pentagon]] Hexagon.svg|[[hexagon]] Heptagon.svg|[[heptagon]] Regular octagon.svg|[[octagon]] Nonagon.svg|[[nonagon|enneagon]] Regular-Decagon.svg|[[decagon]] </gallery>Polygons with more sides look more like [[circles]]. A polygon with an [[Infinity|infinite]] number of sides is called an [[apeirogon]]. Polygons can be described in text by a special symbol called a [[Schläfli symbol]]. This symbol is written as curly brackets, with some numbers inside it, like {3}. {3} is a triangle. The number inside can also be a [[Fraction (mathematics)|fraction]]. A Schläfli symbol of {5/2} is a five-pointed star. == Properties == Most mathematical objects have things that can be said about them that are always true. These are called properties. All polygons (convex and star polygons) can