# Regular polygon

Polygon that is direct equiangular and equilateral (all sides have the same length).

- Regular polygon273 related topics

## Circumscribed circle

Circle that passes through all the vertices of the polygon.

All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.

## Polygon

Plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain .

Regular: both equilateral and equiangular.

## Dihedral group

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

## Perimeter

Closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

The first mathematician known to have used this kind of reasoning is Archimedes, who approximated the perimeter of a circle by surrounding it with regular polygons.

## Incircle and excircles of a triangle

[[Image:Incircle and Excircles.svg|right|thumb|300px|Incircle and excircles of a triangle.

All regular polygons have incircles tangent to all sides, but not all polygons do; those that do are tangential polygons.

## Square

In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles).

## Equilateral triangle

Equilateral triangle is a triangle in which all three sides have the same length.

It is also a regular polygon, so it is also referred to as a regular triangle.

## Hexagon

Six-sided polygon or 6-gon.

A regular hexagon has Schläfli symbol {6} and can also be constructed as a truncated equilateral triangle, t{3}, which alternates two types of edges.

## Octagon

Octagon is an eight-sided polygon or 8-gon.

A regular octagon has Schläfli symbol {8} and can also be constructed as a quasiregular truncated square, t{4}, which alternates two types of edges.

## Uniform polyhedron

In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other).