Tridecagon
A tridecagon or triskaidecagon or trisdecagon or 13-gon is a shape with 13 sides and 13 corners.
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 |
Regular tridecagon
All sides of a regular tridecagon are the same length. Each corner is 147.27°. All corners added together equal 6840°.
Area
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.
Numismatic use
The regular tridecagon is used as the shape of the Czech 20 korun coin.[1]
Tridecagon Media
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.
Related pages
References
- ↑ Colin R. Bruce, II, George Cuhaj, and Thomas Michael, 2007 Standard Catalog of World Coins, Krause Publications, 2006, ISBN 0896894290, p. 81.
Other websites
- Weisstein, Eric W., "Tridecagon" from MathWorld.