Tetracontagon

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

A tetracontagon or 40-gon is a shape with 40 sides and 40 corners.

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

${\text{Area}}=10\left(1+{\sqrt {5}}+{\sqrt {5+2{\sqrt {5}}}}+{\sqrt {\left(1+{\sqrt {5}}+{\sqrt {5+2{\sqrt {5}}}}\right)^{2}+1}}\right)t^{2}$

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].