The regular nonagon is the regular polygon with nine sides and Schläfli symbol .

The regular nonagon cannot be constructed using the classical Greek rules of geometric construction, but Conway and Guy (1996) give a Neusis construction based on angle trisection. Madachy (1979) illustrates how to construct a nonagon by folding and knotting a strip of paper. Although the regular nonagon is not a constructible polygon, Dixon (1991) gives constructions for several angles which are close approximations to the nonagonal angle , including angles of and .

Given a regular nonagon, let be the midpoint of one side, be the mid-arc point of the arc connecting an adjacent side, and the midpoint of . Then, amazingly, (Karst, quoted in Bankoff and Garfunkel 1973).