octogonal

Octogonal is an adjective used to describe something that has eight angles or eight sides, and is largely synonymous with octagonal. In English, octagonal is the more common term in mathematical and geometric contexts, while octogonal appears as a less frequent variant.

In geometry, an octagonal polygon has eight interior angles. For any simple octagon, the sum of interior angles is (8−2)×180 = 1080 degrees. A regular octagon, with eight equal sides and eight equal interior angles, has each interior angle measuring 135 degrees and each exterior angle measuring 45 degrees. The figure possesses eightfold symmetry and, depending on interpretation, can have up to 20 diagonals. The term applies to both convex and concave eight-angled polygons, though most common references describe convex forms.

Octogonal figures occur in various real-world and artistic contexts. A well-known example of a practical octagonal shape is the regular stop sign, which uses eight equal sides. Beyond signage, octagonal forms appear in architectural plans, floor tiling patterns, and decorative motifs where eightfold symmetry or eight-sided geometry is desired. The concept is also relevant in design and crystallography, where eight-angled outlines or profiles may be chosen for aesthetic or functional reasons.

Etymology-wise, octogonal derives from Latin octo- for eight and Greek gonia for angle. The form is occasionally used in English, but octagonal remains the standard adjective for eight-sided geometry.