sexkant

Sexkant is a term used in some languages to denote a six‑sided polygon, commonly known in English as a hexagon. In its regular form, all six sides are equal and all interior angles are equal, each measuring 120 degrees. The sum of interior angles in any hexagon is 720 degrees. A convex sexkant has all interior angles less than 180 degrees; a concave hexagon has at least one interior angle greater than 180 degrees.

For a regular sexkant with side length a, the area is (3√3/2)·a². The distance between opposite sides (the width) is √3·a, while the distance between opposite vertices (the diameter) is 2a. A regular hexagon can be partitioned into six equilateral triangles, revealing its diagonals: there are nine diagonals in total, three of length 2a (connecting opposite vertices) and six of length a√3 (connecting vertices two apart). The symmetry of a regular sexkant is described by the dihedral group D6, consisting of six rotations and six reflections.

Usage and variants: the term sexkant or sekskant is used in Danish and Norwegian to refer to a hexagon; in many contexts the English term hexagon is more common. Beyond the regular form, hexagons can be irregular, convex or concave, with varying side lengths and angles, while still maintaining a total interior angle sum of 720 degrees. Hexagons are notable in tiling and design, and appear in chemistry and nature, such as in the hexagonal arrangement of carbon atoms in benzene rings and in honeycomb structures.