hexagon

An hexagon is a $6$-sided polygon. The most commonly quoted hexagon is a regular (http://planetmath.org/RegularPolygon) hexagon, having congruent sides and congruent interior angles. Below is an example of a regular hexagon:

Below are some properties of regular hexagons in Euclidean geometry:

• The measure (http://planetmath.org/AngleMeasure) of any interior angle of a regular hexagon is ${120}^{\circ }$.

• The smallest $n$ for which a regular $n$-gon has diagonals which are not congruent is $n=6$. For example, in the regular hexagon below, the diagonal drawn in blue and the one drawn in red are not congruent.

• The side of a regular hexagon has the same length as the radius of the circle circumscribing it. This fact is illustrated below.

From the last remark, it is easy to see that a regular hexagon is constructible using compass and straightedge.