sekskant

Sekskant, in geometry, is a polygon with six straight sides and six vertices. In Norwegian, the term sekskant corresponds to the English word hexagon. The interior angle sum of any six‑sided polygon is (6−2)×180 = 720 degrees, and the exterior angles sum to 360 degrees. A regular sekskant is equiangular and equilateral, with all sides equal and all interior angles measuring 120 degrees; irregular sekskanter have unequal sides or angles.

For a regular sekskant with side length a, the perimeter is 6a and the area is (3√3/2) a^2. The hexagon can be partitioned into six equilateral triangles of side a, all sharing a common center. Its diagonals number nine; three of the diagonals connect opposite vertices and pass through the center, forming a central symmetry pattern within the shape. The circumradius and other measurements can be derived from the side length in regular cases.

Symmetry is a key feature: a regular sekskant has dihedral symmetry D6, including six rotations and six reflections. It tessellates the plane, alongside other hexagons, to form the honeycomb pattern used in tiling. This tiling appears in nature, technology, and design, and is a common model in chemistry and crystallography for hexagonal lattices (for example, benzene rings are often depicted on a hexagonal grid).

Irregular sekskanter vary in side lengths and angles and are common in practical applications such as floor tilings and geographic boundaries. The term sekskant is used broadly in math and geometry education to refer to any six‑sided polygon, with regular hexagons represented as the standard case.