Hexadecagon

Regular hexadecagon
Type	Regular polygon
Edges and vertices	16
Schläfli symbol	{16} t{8}
Coxeter–Dynkin diagram
Symmetry group	Dihedral (D16)
Internal angle (degrees)	157.5°
Properties	convex, cyclic, equilateral, isogonal, isotoxal

In mathematics, a hexadecagon (sometimes called a hexakaidecagon) is a polygon with 16 sides and 16 vertices.

Regular hexadecagon

A regular hexadecagon is constructible with a compass and straightedge.

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

Construction

A regular hexadecagon is constructible using compass and straightedge:

Construction of a regular hexadecagon

Area

The area of a regular hexadecagon is: (with t = edge length)

$A = 4t^2 \cot \frac{\pi}{16} = 4t^2 (\sqrt{2}+1)(\sqrt{4-2\sqrt{2}}+1)$

Petrie polygons

The regular hexadecagon is the Petrie polygon for many higher dimensional polytopes, shown in these skew orthogonal projections, including:

A15	15-simplex
B8	8-orthoplex	Rectified 8-orthoplex	Birectified 8-orthoplex	Trirectified 8-orthoplex	Trirectified 8-cube	Birectified 8-cube	Rectified 8-cube	8-cube
D9	t7(161)	t6(161)	t5(161)	t4(161)	t3(161)	t2(161)	t1(161)	9-demicube (161)

External links

• Weisstein, Eric W., "Hexadecagon" from MathWorld.