Kuusnurkaid

Kuusnurkaid are polygons with six sides and six interior angles. The term is Estonian for hexagons, deriving from the roots kuus (six) and nurk (angle). They appear in various geometric contexts and can refer to both regular and irregular six‑sided shapes.

A regular kuusnurk has all sides of equal length and all interior angles measuring 120 degrees. If the side length is s, its perimeter is 6s and its area is (3√3/2)·s². The distance between opposite vertices, the long diagonal, is 2s, and there are shorter diagonals of length √3·s as well. These properties give the hexagon a high degree of symmetry: a regular kuusnurk has 12 symmetries (six rotations and six reflections).

Regular kuusnurkaid tessellate the Euclidean plane, meaning they can cover a flat surface completely without gaps or overlaps. This honeycomb-like tiling is a classical example of efficient plane packing and is often cited in discussions of tiling and lattice structure.

Kuusnurkaid occur in nature and science as well as in design. Bees construct honeycombs with hexagonal cells, a structure that optimizes area and material use. In chemistry and materials science, hexagonal motifs appear in benzene rings and in graphene lattices. Architecture and graphic design frequently employ hexagonal patterns for their aesthetic clarity and functional tiling properties.

Hexagons may be irregular as well; in any hexagon, the sum of interior angles is always 720 degrees, but only the regular hexagon has equal sides and equal angles.