Icosagon
| Regular icosagon | |
|---|---|
A regular icosagon
|
|
| Type | Regular polygon |
| Edges and vertices | 20 |
| Schläfli symbol | {20}, t{10}, tt{5} |
| Coxeter diagram |
   
|
| Symmetry group | Dihedral (D20), order 2×20 |
| Internal angle (degrees) | 162° |
| Dual polygon | Self |
| Properties | Convex, cyclic, equilateral, isogonal, isotoxal |
In geometry, an icosagon or 20-gon is a twenty-sided polygon. The sum of any icosagon's interior angles is 3240 degrees.
The regular icosagon has Schläfli symbol {20}, and can also be constructed as a truncated decagon, t{10}, or a twice-truncated pentagon, tt{5}.
One interior angle in a regular icosagon is 162°, meaning that one exterior angle would be 18°.
The area of a regular icosagon with edge length t is
In terms of the radius R of its circumcircle, the area is
since the area of the circle is the regular icosagon fills approximately 98.36% of its circumcircle.
The Big Wheel on the popular US game show The Price Is Right has an icosagonal cross-section.
The Globe, the outdoor theater used by William Shakespeare's acting company, was discovered to have been built on an icosagonal foundation when a partial excavation was done in 1989.
As a golygonal path, the swastika is considered to be an irregular icosagon.
A regular square, pentagon, and icosagon can completely fill a plane vertex.
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