enneaheptagon

An enneaheptagon is a polygon with nineteen sides and nineteen vertices, classified as a nonadecagon in some mathematical contexts due to its nineteen-sided nature. The term "enneaheptagon" combines the Greek numerical prefixes *ennea-* (nine) and *hepta-* (seven), which together incorrectly suggest nineteen sides (9 + 7 = 16), but it is sometimes used colloquially or in informal contexts to refer to a 19-sided figure. The more precise and widely accepted term for a polygon with nineteen sides is *nonadecagon*, derived from *nona-* (nine) and *dec-* (ten), reflecting the correct total of nineteen edges.

An enneaheptagon is a type of cyclic polygon if all its vertices lie on a single circle, and it can be either convex or concave. The interior angle of a regular enneaheptagon (one with equal sides and angles) can be calculated using the formula for regular *n*-sided polygons: ((n − 2) × 180°) / n. For a nonadecagon, this yields approximately 166.32°. The exterior angle of a regular enneaheptagon is 360° divided by nineteen, resulting in roughly 18.95°.

Constructing a regular enneaheptagon with straightedge and compass alone is not feasible due to its sides not being constructible with these tools, as nineteen is not a Fermat prime. However, approximations can be made using geometric techniques or computational methods. Enneaheptagons appear in advanced geometry, tiling studies, and theoretical mathematics, particularly in the analysis of high-order polygons and their properties.

In practical applications, polygons with nineteen sides are rare due to their complexity, but they serve as useful examples in mathematical research, particularly in the study of polygon symmetry, tiling, and geometric constructions.