Pentadecagon
| 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 |
A pentadecagon or quindecagon or 15-gon is a shape with 15 sides and 15 corners.
Regular pentadecagon[change]
All sides of a regular pentadecagon are the same length. Each corner is 156°. All corners added together equal 2340°.
Area[change]
The amount of space a regular pentadecagon takes up is
- <math>
\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[change]
File:3.10.15 vertex.png
A regular triangle, decagon, and pentadecagon can completely fill a plane vertex.
