Triskaidecagon

Regular tridecagon
A regular triskaidecagon
Type	Regular polygon
Edges and vertices	13
Schläfli symbol	{13}
Coxeter–Dynkin diagram
Symmetry group	Dihedral (D13)
Internal angle (degrees)	$\approx 152.308$°
Properties	convex, cyclic, equilateral, isogonal, isotoxal

In geometry, a tridecagon (or triskaidecagon) is a polygon with 13 sides and angles.

Regular triskaidecagon

The measure of each internal angle of a regular triskaidecagon is approximately 152.308 degrees, and the area with side length a is given by

$A = \frac{13}{4}a^2 \cot \frac{\pi}{13} \simeq 13.1858\,a^2.$

Related polygons

A triskaidecagram is a 13-sided star polygon. There are 5 regular forms given by Schläfli symbols: {13/2}, {13/3}, {13/4}, {13/5}, {13/6}.

Construction

A regular triskaidecagon is not constructible with compass and straightedge. However, it is constructible using a Neusis construction.

Petrie polygons

The regular triskaidecagon is the Petrie polygon for a number of higher dimensional polytope, projected in a skew orthogonal projection, including from the A₁₂, 12-simplex family:

A12	12-simplex	Rectified 12-simplex	Birectified 12-simplex	trirectified 12-simplex	quadrirectified 12-simplex	quintirectified 12-simplex

External links

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