Tetracontagon
A tetracontagon or 40-gon is a shape with 40 sides and 40 corners.
| Regular tetracontagon | |
|---|---|
 A 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.
When calculating polygonal numbers (numbers that can be represented as a regular polygon),
typically stands for a Triangular Number [1.4.9].
The formula to find the
40-gonal number (
) is often expressed using the
and triangular numbers:
In this context,
is the triangular number, calculated as [1.3.7, 1.4.9].
Tetracontagon Media
Some polygons of different kinds: open (excluding its boundary), boundary only (excluding interior), closed (including both boundary and interior), and self-intersecting.
Some different types of polygon
Partitioning an n-gon into n − 2 triangles
Coordinates of a non-convex pentagon
Historical image of polygons (1699)
The Giant's Causeway, in Northern Ireland
