pluralsidedness

Pluralsidedness is the descriptive property of having multiple sides. In geometry, it is commonly used to refer to polygons with more than two sides, typically expressed as n-gons, where n is a positive integer. In Euclidean plane geometry a true digon (two sides) is degenerate, so pluralsided figures usually begin at three sides (triangles). The term is informal, and formal discussions typically use polygon or n-gon terminology, but pluralsidedness remains a convenient shorthand for the general case of many-sided figures.

For an n-sided polygon, the sum of interior angles is (n − 2) × 180 degrees, there are n sides and n vertices, and regular polygons have equal sides and angles while irregular ones do not. Pluralsidedness influences geometric properties such as symmetry, edge length distribution, and the ways a figure can be tiled or triangulated. It is a consideration in fields like computer graphics, architectural design, and computational geometry, where the number of sides constrains algorithms, rendering, and construction.

On curved surfaces, polygonal regions can exhibit non-Euclidean variations, and concepts such as digons may appear in spherical or hyperbolic geometry. In three dimensions, pluralsided polygons occur as faces of polyhedra and in mesh models, where the side count and arrangement of each face affect mesh quality, stability, and rendering.

See also: polygon, n-gon, digon, tiling, polyhedron.