A closed two-dimensional polygon bounded by eight straight-line segments.The formula with which to find an equilateral octagon's area is 4.8284 times the length of one side squared.Examples used in art:Frans Hals (Dutch, born after 1580, died 1666), The Smoker, c. 1623-25, oil on wood panel, octagonal, 18 3/8 x 19 1/2 inches (46.7 x 49.5 cm), Metropolitan Museum of Art, NY. The octagonal shape of this panel is original. Alessandro Algardi (Italian, 1598-1654), Piet?, 1630-40, octagonal bronze relief (a rectangular frame conceals corners), excluding flange: 11 3/4 x 11 3/4 inches (29.8 x 29.8 cm), Frick Collection, NY. See Piet?.Also see mathematics, radial, and shape.