Icosagon facts for kids
Quick facts for kids Regular icosagon |
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A regular icosagon
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| 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 |
An icosagon is a shape with 20 sides and 20 corners. It has interior angles of 162 and exterior angles of 198.
Regular icosagon
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}.
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 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.
Dissection
Coxeter states that every parallel-sided 2m-gon can be divided into m(m-1)/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 10-cube, with 45 of 11520 faces. The list A006245 enumerates the number of solutions as 18,410,581,880, including up to 20-fold rotations and chiral forms in reflection.
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Images for kids
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Icosagon with given side length, animation (The construction is very similar to that of decagon with given side length)
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Symmetries of a regular icosagon. Vertices are colored by their symmetry positions. Blue mirrors are drawn through vertices, and purple mirrors are drawn through edge. Gyration orders are given in the center.
See also
In Spanish: Isodecágono para niños
