Pentadecagon
A pentadecagon or quindecagon or 15-gon is a shape with 15 sides and 15 corners.
| Regular pentadecagon | |
|---|---|
| File:Pentadecagon.svg A regular pentadecagon | |
| Type | Regular polygon |
| Edges and vertices | 15 |
| Schläfli symbol | {15} |
| Coxeter diagram | File:CDel node 1.pngFile:CDel 15.pngFile:CDel node.png |
| Symmetry group | Dihedral (D15), order 2×15 |
| Internal angle (degrees) | 156° |
| Dual polygon | Self |
| Properties | Convex, cyclic, equilateral, isogonal, isotoxal |
Regular pentadecagon
All sides of a regular pentadecagon are the same length. Each corner is 156°. All corners added together equal 2340°.
Area
The amount of space a regular pentadecagon takes up is
- [math]\displaystyle{ \begin{align} A = \frac{15}{4}a^2 \cot \frac{\pi}{15} & = \frac{15}{4}\sqrt{7+2\sqrt{5}+2\sqrt{15+6\sqrt{5}}}a^2 \\ & = \frac{15a^2}{8} \left( \sqrt{3}+\sqrt{15}+ \sqrt{2}\sqrt{5+\sqrt{5}} \right) \\ & \simeq 17.6424\,a^2. \end{align} }[/math]
a is the length of one of its sides.
Uses
160px
A regular triangle, decagon, and pentadecagon can completely fill a plane vertex.
Pentadecagon Media
- Regular Pentadecagon Inscribed in a Circle.gif
Regular Pentadecagon Inscribed in a Circle
- 01-Fünfzehneck.svg
Pentadecagon
- 01-FünfzehneckAnimation.gif
Pentadecagon, animation
- Symmetries of pentadecagon.png
The symmetries of a regular pentadecagon as shown with colors on edges and vertices. Lines of reflections are blue. Gyrations are given as numbers in the center. Vertices are colored by their symmetry positions.
- Regular star polygon 15-2.svg
en:Star polygon
- Regular star figure 3(5,1).svg
Regular star figure 3(5,1)
- Regular star polygon 15-4.svg
en:Star polygon
- Regular star figure 5(3,1).svg
Regular star figure 5(3,1)
- Regular star figure 3(5,2).svg
Regular star figure 3(5,2)
- Regular star polygon 15-7.svg
en:Star polygon