pentagon

A pentagon is a 5-sided planar polygon.

Regular pentagons are of particular interest for geometers.On a regular pentagon, the inner angles are equal to ${108}^{\circ }$.All ten diagonals have the same length. If $s$ is the length of a side and $d$ is the length of a diagonal, then

$$\frac{d}{s}=\frac{1+\sqrt{5}}{2};$$

that is, the ratio between a diagonal and a side is the Golden Number.

A regular pentagon (along with its diagonals) can also be obtained asthe projection of a regular pentahedron in four dimensional spaceonto a plane determined by two opposite edges.This is analogous to the way a square with its diagonals can be obtainedas the projection of a tetrahedrononto a plane determined by two opposite edges.