polygoneiden

Polygoneiden is the genitive plural form of the term polygon in Finnish, used when referring to multiple polygons in mathematical text. It appears in phrases such as polygoneiden ominaisuudet (the properties of polygons) or polygoneiden rajoja koskevat määritelmät (definitions relating to the boundaries of polygons). The form signals possession or relation to more than one polygon.

A polygon is a closed planar figure formed by a finite sequence of straight line segments, called sides, that meet at endpoints called vertices. The sides connect to form a single, non-intersecting circuit. Polygons are classified by the number of sides and by shape properties. Common categories include triangles (three sides), quadrilaterals (four sides), and, more generally, n-gons for polygons with n sides. A polygon is convex if all interior angles are less than 180 degrees and every line segment between two points in the polygon lies entirely inside it; otherwise it is concave.

Regular polygons have all sides and all interior angles equal, with the square and the equilateral triangle among the simplest examples. The interior angle sum of an n-gon is (n−2)×180 degrees, and the number of diagonals is n(n−3)/2. Simple polygons do not cross themselves; self-intersecting polygons, sometimes called star polygons, are non-simple.

Polygons are foundational in geometry and appear in various applications, including computer graphics, architectural design, and tiling problems. They also provide a gateway to more advanced topics such as polygonal numbers, mesh generation, and planar graphs.