Hexadecagon

Regular hexadecagon
A regular hexadecagon
Type	Regular polygon
Edges and vertices	16
Schläfli symbol	{16}, t{8}, tt{4}
Coxeter diagram
Symmetry group	Dihedral (D16), order 2×16
Internal angle (degrees)	157.5°
Dual polygon	Self
Properties	Convex, cyclic, equilateral, isogonal, isotoxal

In mathematics, a hexadecagon (sometimes called a hexakaidecagon) or 16-gon is a sixteen-sided polygon.

A regular hexadecagon is a hexadecagon in which all angles are equal and all sides are congruent. Its Schläfli symbol is {16} and can be constructed as a truncated octagon, t{8}, and a twice-truncated square tt{4}. A truncated hexadecagon, t{16}, is a triacontadigon, {32}.

As 16 = 2⁴ (a power of two), a regular hexadecagon is constructible using compass and straightedge: this was already known to ancient Greek mathematicians.

Each angle of a regular hexadecagon is 157.5 degrees, and the total angle measure of any hexadecagon is 2520 degrees.

The area of a regular hexadecagon with edge length t is

Because the hexadecagon has a number of sides that is a power of two, its area can be computed in terms of the circumradius R by truncating Viète's formula:

Since the area of the circumcircle is ${\displaystyle \pi R^{2},}$ the regular hexadecagon fills approximately 97.45% of its circumcircle.

The regular hexadecagon has Dih₁₆ symmetry, order 32. There are 4 dihedral subgroups: Dih₈, Dih₄, Dih₂, and Dih₁, and 5 cyclic subgroups: Z₁₆, Z₈, Z₄, Z₂, and Z₁, the last implying no symmetry.