Icosagon facts for kids
Regular icosagon  

A regular icosagon


Type  Regular polygon 
Edges and vertices  20 
Schläfli symbol  {20}, t{10}, tt{5} 
Coxeter diagram  
Symmetry group  Dihedral (D_{20}), order 2×20 
Internal angle (degrees)  162° 
Dual polygon  Self 
Properties  Convex, cyclic, equilateral, isogonal, isotoxal 
An icosagon is a shape with 20 sides and 20 corners. It has interior angles of 162 and exterior angles of 198.
Contents
Regular icosagon
The regular icosagon has Schläfli symbol {20}, and can also be constructed as a truncated decagon, t{10}, or a twicetruncated pentagon, tt{5}.
Area
The amount of space a regular icosagon takes up is
a is the length of one of its sides.
Uses
The Big Wheel on the popular US game show The Price Is Right has an icosagonal crosssection.
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.
Dissection
Coxeter states that every parallelsided 2mgon can be divided into m(m1)/2 rhombs. For the icosagon, m=10, and it can be divided into 45: 5 squares and 4 sets of 10 rhombs. This decomposition is based on a Petrie polygon projection of a 10cube, with 45 of 11520 faces. The list A006245 enumerates the number of solutions as 18,410,581,880, including up to 20fold rotations and chiral forms in reflection.

Images for kids

Icosagon with given side length, animation (The construction is very similar to that of decagon with given side length)