The nonagon, also known as an enneagon, is a 9-sided polygon. Although the term "enneagon" is perhaps preferable (since it uses the Greek prefix and suffix instead of the mixed Roman/Greek nonagon), the term "nonagon," which is simpler to spell and pronounce, is used in this work.
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).
Bankoff, L. and Garfunkel, J. "The Heptagonal Triangle." Math. Mag. 46,
7-19, 1973.
Bold, B. Famous Problems of Geometry and How to Solve Them. New
York: Dover, pp. 60-61, 1982.
Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 194-200,
1996.
Dixon, R. Mathographics. New York: Dover, pp. 40-44, 1991.
Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 60-61,
1979.
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