Enneadecagon

Regular enneadecagon
A regular enneadecagon
Type	Regular polygon
Edges and vertices	19
Schläfli symbol	{19}
Coxeter–Dynkin diagram
Symmetry group	Dihedral (D19)
Internal angle (degrees)	$\approx 161.052$°
Properties	convex, cyclic, equilateral, isogonal, isotoxal

In geometry, an enneadecagon is a polygon with 19 sides and angles. It is also known as an enneakaidecagon or a nonadecagon.

The radius of the circumcircle of the regular enneadecagon with side length t is

$R=\frac{t}{2} \csc \frac {180}{19}$ (angle in degrees)

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

$\frac{19}{4}t^2 \cot \frac{\pi}{19}$
$\simeq 28.4652\,t^2.$

Construction

A regular enneadecagon cannot be constructed using a compass and straightedge.

Petrie polygons

The regular enneadecagon is the Petrie polygon for one higher dimensional polytope, projected in a skew orthogonal projection:

18-simplex (18D)

External links

• Weisstein, Eric W., "Enneadecagon" from MathWorld.