Pentadecagon
| Regular pentadecagon | |
|---|---|
A regular pentadecagon |
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| Edges and vertices | 15 |
| Schläfli symbol | {15} |
| Coxeter–Dynkin diagrams | |
| Symmetry group | Dihedral (D15) |
| Internal angle (degrees) | 156° |
| Properties | convex, cyclic, equilateral, isogonal, isotoxal |
In geometry, a pentadecagon (or pentakaidecagon) is any 15-sided, 15-angled, polygon.
Contents |
Regular pentadecagon
A regular pentadecagon has interior angles of 156°, and with a side length a, has an area given by
Construction
A regular pentadecagon is constructible using compass and straightedge:
Construction of a regular pentadecagon
Pentadecagrams
There are 3 regular star polygons: {15/2}, {15/4}, {15/7}, constructed from the same 15 vertices of a regular pentadecagon, but connected by skipping every second, forth, or seventh vertex respectively.
There are also three regular star figures: {15/3}, {15/5}, {15/6}, the first being a compound of 3 pentagons, the second a compound of 5 equilateral triangles, and the third is a compound of 3 pentagrams.
Petrie polygons
The regular pentadecagon is the Petrie polygon for one higher dimensional polytope, projected in a skew orthogonal projection:
14-simplex (14D) |
External links
- Weisstein, Eric W., "Pentadecagon" from MathWorld.
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