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Chiliagon facts for kids

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Regular chiliagon
Chiliogon.svg
A regular chiliagon
Type Regular polygon
Edges and vertices 1000
Schläfli symbol {1000}, t{500}, tt{250}, ttt{125}
Coxeter diagram CDel node 1.pngCDel 10.pngCDel 0x.pngCDel 0x.pngCDel node.png
CDel node 1.pngCDel 5.pngCDel 0x.pngCDel 0x.pngCDel node 1.png
Symmetry group Dihedral (D1000), order 2×1000
Internal angle (degrees) 179.64°
Dual polygon Self
Properties Convex, cyclic, equilateral, isogonal, isotoxal

A chiliagon or 1000-gon is a shape with 1000 sides and 1000 corners.

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

A = 250a^2 \cot \frac{\pi}{1000} \simeq 79577.2\,a^2

a is the length of one of its sides.

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