240-gon

Regular 240-gon
Type	Regular polygon
Edges and vertices	240
Schläfli symbol	{240}, t{120}, tt{60}, ttt{30}
Coxeter diagram
Symmetry group	Dihedral (D240), order 2×240
Internal angle (degrees)	178.5°
Dual polygon	Self
Properties	Convex, cyclic, equilateral, isogonal, isotoxal

In geometry, a 240-gon is a polygon with 240 sides. The sum of any 240-gon's interior angles is 42840 degrees.

Regular 240-gon properties

A regular 240-gon is represented by Schläfli symbol {240} and also can be constructed as a truncated 120-gon, t{120}, or a twice-truncated 60-gon, tt{60}, or a thrice-truncated 30-gon, ttt{30}.

One interior angle in a regular 240-gon is 178.5°, meaning that one exterior angle would be 1.5°.

The area of a regular 240-gon is (with t = edge length)

$A=60t^{2}\cot {\frac {\pi }{240}}$

and its inradius is

$r={\frac {1}{2}}t\cot {\frac {\pi }{240}}$

The circumradius of a regular 240-gon is

$R={\frac {1}{2}}t\csc {\frac {\pi }{240}}$

This means that the trigonometric functions of π/240 can be expressed in radicals.

Constructible

Since 240 = 2⁴ × 3 × 5, a regular 120-gon is constructible using a compass and straightedge. As a truncated hexacontagon, it can be constructed by an edge-bisection of a regular 120-gon.

References

This article "240-gon" is from Wikipedia. The list of its authors can be seen in its historical and/or the page Edithistory:240-gon. Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one.

📰 Article(s) of the same category(ies)

• Hexacontagon
• 720-gon
• 144-gon
• Tetracontaoctagon
• Triacontadigon
• Octacontagon
• 180-gon

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