eightsided

Eightsided is an adjective used in geometry to describe objects that have eight sides. In two dimensions, the eight-sided polygon is most commonly called an octagon; eightsided is used descriptively when a formal name is not specified. In three dimensions, the phrase can be misleading, since eight-sided typically refers to planar shapes, while eight-faced solids are polyhedra; a familiar example is the regular octahedron, which has eight faces but is not an eight-sided polygon.

For polygons, the sum of interior angles of an eight-sided figure is (8 − 2) × 180 = 1080 degrees. In a regular octagon, all sides and all interior angles are equal, so each interior angle measures 135 degrees and each exterior angle measures 45 degrees. The number of diagonals in an eight-sided polygon is n(n − 3)/2 = 8 × 5 / 2 = 20. The perimeter of a regular octagon with side length s is 8s, and its area is A = 2(1 + √2) s². If the circumradius or apothem is known, alternative area expressions can be used.

Regular octagons appear in practical and decorative contexts. Stop signs in many countries use a regular octagonal shape for recognizability and standardization. In architecture and design, octagonal motifs provide symmetry and visual interest. In education and mathematics, eight-sided polygons serve as straightforward examples of polygons with eight sides, illustrating concepts such as angle sums, diagonals, and area calculations. In contrast, eight-faced solids in three dimensions (such as the regular octahedron) are distinct from eight-sided polygons.