Tetradecagon

Regular tetradecagon
Type	Regular polygon
Edges and vertices	14
Schläfli symbol	{14} t{7}
Coxeter–Dynkin diagram
Symmetry group	Dihedral (D14)
Internal angle (degrees)	180 × (6 / 7) degrees $\simeq 154.2857^\circ$
Properties	convex, cyclic, equilateral, isogonal, isotoxal

In geometry, a tetradecagon (or tetrakaidecagon) is a polygon with 14 sides and angles.

Regular tetradecagon

The area of a regular tetradecagon of side length a is given by

$A = \frac{14}{4}a^2\cot\frac{\pi}{14}\simeq 15.3345a^2$

Construction

A regular tetradecagon cannot be constructed using a compass and straightedge. The animation below gives an approximation of about 0.05° on the center angle:

Construction of an approximated regular tetradecagon

Petrie polygons

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

A13	13-simplex
BC7	7-orthoplex	Rectified 7-orthoplex	Birectified 7-orthoplex	Trirectified 7-cube	Birectified 7-cube	Rectified 7-cube	7-cube
BC7	(421)	t1(421)	t2(421)	t3(421)	(241)	t1(241)	(142)
D8	t6(151)	t5(151)	t4(151)	t3(151)	t2(151)	t1(151)	(151)

External links

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