Tetracontagon
A tetracontagon or 40-gon is a shape with 40 sides and 40 corners.
Regular tetracontagon | |
---|---|
Type | Regular polygon |
Edges and vertices | 40 |
Schläfli symbol | {40}, t{20}, tt{10}, ttt{5} |
Coxeter diagram | |
Symmetry group | Dihedral (D40), order 2×40 |
Internal angle (degrees) | 171° |
Dual polygon | Self |
Properties | Convex, cyclic, equilateral, isogonal, isotoxal |
Regular tetracontagon
All sides of a regular tetracontagon are the same length. Each corner is 171°. All corners added together equal 6840°.
Area
The amount of space a regular tetracontagon takes up is
- [math]\displaystyle{ \text{Area} = 10\left(1+\sqrt{5}+\sqrt{5+2\sqrt{5}}+\sqrt{\left(1+\sqrt{5}+\sqrt{5+2\sqrt{5}}\right)^2+1}\right)t^2 }[/math]
a is the length of one of its sides.