Tridecagon

Regular 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

A tridecagon or triskaidecagon or trisdecagon or 13-gon is a shape with 13 sides and 13 corners.

Regular tridecagon

All sides of a regular tridecagon are the same length. Each corner is 147.27°. All corners added together equal 6840°.

The amount of space a regular tridecagon takes up is

[math]\displaystyle{ A = \frac{13}{4}a^2 \cot \frac{\pi}{13} \simeq 13.1858\,a^2. }[/math]

a is the length of one of its sides.

The regular tridecagon is used as the shape of the Czech 20 korun coin.^[1]

A regular tridecagon (triskaidecagon) with radius of circumcircle \overline{OA} = 12 as an animation (1 min 44 s),*angle trisection by means of the Tomahawk (light blue). This construction is derived from the following equation:12\cos\left(\frac{2\pi}{13}\right)=2\sqrt{26-2\sqrt{13}}\cos\left(\frac{1}{3}\arctan\left(\frac{\sqrt{3}\left(\sqrt{13}+1\right)}{7-\sqrt{13}}\right)\right)+\sqrt{13}-1.
An Approximate Tridecagon Construction.
Tridecagon, approximate construction as an animation (3 min 30 s)
Symmetries of a regular tridecagon. Vertices are colored by their symmetry positions. Blue mirrors are drawn through vertices and edge. Gyration orders are given in the center.
20 Czech koruna (korun českých)
en:Star polygon
en:Star polygon
en:Star polygon
en:Star polygon
en:Star polygon