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).
