heksagon

heksagon, or hexagon in English, is a polygon with six sides and six vertices. The name comes from the Greek words hex, six, and gonia, angle. The term heksagon is used in some European languages as a direct cognate.

There are regular and irregular hexagons; convex and concave forms are possible. A hexagon has an interior angle sum of 720 degrees. In a regular hexagon each interior angle is 120 degrees. The number of diagonals in a hexagon is 9.

In a regular hexagon, the shape can be divided into six equilateral triangles; the side length a equals the radius of the circumscribed circle. Perimeter P equals 6a. Area A equals (3√3/2) a^2. If the hexagon is inscribed in a circle of radius R, the area also equals (3√3/2) R^2.

Hexagons tile the plane without gaps in a honeycomb pattern, because 120-degree angles fit three around each vertex. This tiling is common in both nature and design.

In chemistry, hexagons appear in the benzene ring, a hexagonal arrangement of carbon atoms. In architecture and design, hexagonal grids and tessellations are used for flooring, tiling, and decorative motifs.