kuusikulmagridi

A kuusikulmagridi, literally translating from Finnish as “six‑sided grid”, is a tessellation of the Euclidean plane using regular hexagons. Each hexagon shares its edges with six neighboring hexagons, resulting in a highly regular, repeating pattern that fills the plane without gaps or overlaps. The term is used primarily in Finnish mathematical literature and engineering contexts, where it is often synonymous with the English “hexagonal grid” or “hexagonal lattice”.

The hexagonal grid is one of the three regular tilings of the plane, alongside the square and triangular tilings. Its vertices form a triangular lattice, while its center‑to‑center distances form a hexagonal lattice. Because of its high symmetry, it appears naturally in many physical systems such as the arrangement of cells in a honeycomb, the packing of atoms in graphene, and the layout of certain cellular automata.

In computer graphics and scientific visualization, a hexagonal grid provides advantages over a rectangular grid for sampling and interpolation. For example, in geographic information systems, hexagonal tiling reduces distortion when covering large areas of the Earth's surface. In computational geometry, algorithms for pathfinding and nearest‑neighbour searching can exploit the equidistant spacing of hexagonal nodes to achieve more uniform coverage.

Mathematically, the hexagonal lattice can be described by the basis vectors (1,0) and (½, √3/2) in two‑dimensional Euclidean space. The dual lattice, obtained by connecting the centres of adjacent hexagons, is also the hexagonal lattice, making it a self‑dual tiling. The grid is widely used in crystallography, materials science, and the study of quasicrystals due to its efficient packing properties and six‑fold rotational symmetry.