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The intersection of a triangle's internal angle bisectors. It is the center of the circle tangent to all three sides, and its distance to any side is the inradius.

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.