| Regular tridecagon | |
|---|---|
 A regular tridecagon |
|
| Type | Regular polygon |
| Edges and vertices | 13 |
| Schläfli symbol | {13} |
| Coxeter–Dynkin diagram |    |
| Symmetry group | Dihedral (D13), order 2×13 |
| Internal angle (degrees) |
Failed to parse (Missing texvc executable; please see math/README to configure.): \approx 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.
Contents |
Regular tridecagon [link]
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
- Failed to parse (Missing texvc executable; please see math/README to configure.): A = \frac{13}{4}a^2 \cot \frac{\pi}{13} \simeq 13.1858\,a^2.
Numismatic use [link]
The regular tridecagon is used as the shape of the Czech 20 korun coin.[1]
Related polygons [link]
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}, {13/6}.
Construction [link]
A regular tridecagon is not constructible with compass and straightedge. However, it is constructible using a Neusis construction.[2]
Petrie polygons [link]
The regular tridecagon 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 |
|---|
References [link]
- ^ Colin R. Bruce, II, George Cuhaj, and Thomas Michael, 2007 Standard Catalog of World Coins, Krause Publications, 2006, ISBN 0896894290, p. 81.
- ^ AM Gleason (1988), "Angle trisection, the heptagon, and the triskaidecagon," Amer. Math. Monthly, 95(3).
External links [link]
- Weisstein, Eric W., "Tridecagon" from MathWorld.
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