Tridecagon

Regular tridecagon
A regular tridecagon
Type	Regular polygon
Edges and vertices	13
Schläfli symbol	{13}
Coxeter diagram
Symmetry group	Dihedral (D13), order 2×13
Internal angle (degrees)	≈152.308°
Dual polygon	Self
Properties	Convex, cyclic, equilateral, isogonal, isotoxal

In geometry, a tridecagon or triskaidecagon or 13-gon is a thirteen-sided polygon.

As 13 is a Pierpont prime but not a Fermat prime, the regular tridecagon cannot be constructed using a compass and straightedge. However, it is constructible using neusis, or an angle trisector.

The following is an animation from a neusis construction of a regular tridecagon with radius of circumcircle ${\displaystyle {\overline {OA}}=12,}$ according to Andrew M. Gleason, based on the angle trisection by means of the Tomahawk (light blue).

An approximate construction of a regular tridecagon using straightedge and compass is shown here.

Another possible animation of an approximate construction, also possible with using straightedge and compass.

GeoGebra: ${\displaystyle \scriptstyle \angle {}}$BME₁ = 27.692307692307764°