 Regular hexagon

A regular hexagon is a hexagon with all side lengths equal and all interior angles equal to $2\pi /3$. Joining its centre to the six vertices divides it into six equilateral triangles. Consequently its circumradius equals its side length $a$, its inradius is $\sqrt{3}a/2$, and its area is $3\sqrt{3}{a}^2/2$. Three regular hexagons meet around a vertex because $3(2\pi /3)=2\pi$, producing the familiar edge-to-edge tessellation of the Euclidean plane.