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240-gon

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Regular 240-gon
Type Regular polygon
Edges and vertices 240
Schläfli symbol {240}, t{120}, tt{60}, ttt{30}
Coxeter diagram CDel node 1.pngCDel 2x.pngCDel 4.pngCDel 0x.pngCDel node.png
CDel node 1.pngCDel 12.pngCDel 0x.pngCDel node 1.png
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[edit | edit source]

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)

<math>A = 60t^2 \cot \frac{\pi}{240}</math>

and its inradius is

<math>r = \frac{1}{2}t \cot \frac{\pi}{240}</math>

The circumradius of a regular 240-gon is

<math>R = \frac{1}{2}t \csc \frac{\pi}{240}</math>

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

Constructible[edit | edit source]

Since 240 = 24 × 3 × 5, a regular 120-gon is constructible using a compass and straightedge.[1] As a truncated hexacontagon, it can be constructed by an edge-bisection of a regular 120-gon.

References[edit | edit source]


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