esagonale

Esagonale is an Italian term meaning hexagonal, used to describe objects or figures with six sides or sixfold symmetry. In geometry, esagonale corresponds to the English word hexagonal. A polygon with six sides is called a esagonale or hexagon; a regular esagonale has all sides and all interior angles equal.

A simple esagonale has an interior angle sum of (6 − 2) × 180 = 720 degrees. Consequently, the exterior angles sum to 360 degrees. Convex esagonali have all interior angles less than 180 degrees, while concave forms exist as well. The number of diagonals in a hexagon is n(n − 3)/2, which for n = 6 gives nine diagonals.

Regular esagonali have additional symmetric properties: all six sides are equal and all interior angles are 120 degrees. If the side length is a, the circumradius (distance from the center to a vertex) equals a, the apothem is a√3/2, and the area is A = (3√3/2) a^2. The three distinct diagonals in a regular hexagon have lengths a√3 (between vertices two apart) and 2a (between opposite vertices).

Applications and occurrences: esagonali are central in plane tiling, as regular hexagons tessellate the plane without gaps. They appear in crystallography and chemistry, where hexagonal symmetry or lattice structures are described as esagonale in Italian texts. The term also appears in geometry and design, where sixfold symmetry underpins certain tilings and molecular shapes.

See also: hexagon, regular polygon, hexagonal tiling, hexagonal lattice.