# 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) is a polygon with 13 sides and angles.

A regular tridecagon is represented by Schläfli symbol {13}.

## Regular tridecagon

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

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

### Numismatic use

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

## Related polygons

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

 Picture Internal angle {13/2} {13/3} {13/4} {13/5} {13/6} ≈124.615° ≈96.9231° ≈69.2308° ≈41.5385° ≈13.8462°

## Construction

An Approximate Tridecagon using Straightedge and compass is shown here.

Another animation of an approximate construction:

• Example illustrating the error: At a radius r = 100 million km, the absolute error of the 1st side would be approximately -2,85 mm.
• For details, see:

### Petrie polygons

The regular tridecagon is the Petrie polygon 12-simplex:

A12

12-simplex

## References

1. ^ Colin R. Bruce, II, George Cuhaj, and Thomas Michael, 2007 Standard Catalog of World Coins, Krause Publications, 2006, ISBN 0896894290, p. 81.