In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, an enneadecagon is a polygon

Polygon

In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...

 with 19 sides and angles. It is also known as an enneakaidecagon or a nonadecagon.

The radius of the circumcircle of the regular

Regular polygon

A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...

 enneadecagon with side length t is

(angle in degrees)

The area of a regular enneadecagon, where t is the edge length, is

Construction

A regular enneadecagon cannot be constructed

Constructible polygon

In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not....

 using compass and straightedge

Compass and straightedge

Compass-and-straightedge or ruler-and-compass construction is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass....

.

Petrie polygons

The regular enneadecagon is the Petrie polygon

Petrie polygon

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon such that every consecutive sides belong to one of the facets...

 for one higher dimensional polytopes, projected in a skew orthogonal projection:

18-simplex (18D)