Chiliagon
A chiliagon or 1000-gon is a shape with 1000 sides and 1000 corners.
| Regular chiliagon | |
|---|---|
 A regular chiliagon | |
| Type | Regular polygon |
| Edges and vertices | 1000 |
| Schläfli symbol | {1000}, t{500}, tt{250}, ttt{125} |
| Coxeter diagram |      |
| Symmetry group | Dihedral (D1000), order 2×1000 |
| Internal angle (degrees) | 179.64° |
| Dual polygon | Self |
| Properties | Convex, cyclic, equilateral, isogonal, isotoxal |
Regular chiliagon
A regular chiliagon is represented by Schläfli symbol {1000} and can be constructed as a truncated 500-gon, t{500}, or a twice-truncated 250-gon, tt{250}, or a thrice-truncated 125-gon, ttt{125}.
Area
The amount of space a regular chiliagon takes up is
- [math]\displaystyle{ A = 250a^2 \cot \frac{\pi}{1000} \simeq 79577.2\,a^2 }[/math]
a is the length of one of its sides.
Chiliagon Media
A whole regular chiliagon is not visually discernible from a circle. The lower section is a portion of a regular chiliagon, 200 times as large as the smaller one, with the vertices highlighted.
The symmetries of a regular chiliagon. Light blue lines show subgroups of index 2. The 4 boxed subgraphs are positionally related by index 5 subgroups.
Regular star polygon {1000/499
Star_polygon_1000-499_center
