TypeRegular polygon
Edges and vertices14
Schläfli symbol{14}, t{7}
Coxeter diagram
Symmetry groupDihedral (D14), order 2×14
Internal angle (degrees)≈154.2857°
Dual polygonSelf
PropertiesConvex, cyclic, equilateral, isogonal, isotoxal

A tetradecagon or 14-gon is a shape with 14 sides and 14 corners.

## Contents

A regular tetradecagon has Schläfli symbol {14} and can be constructed as a quasiregular truncated heptagon, t{7}, which alternates two types of edges.

### Area

The amount of space a regular tetradecagon takes up is

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

{\displaystyle {\begin{aligned}A&={\frac {14}{4}}a^{2}\cot {\frac {\pi }{14}}={\frac {14}{4}}a^{2}\left({\frac {{\sqrt {7}}+4{\sqrt {7}}\cos \left({{\frac {2}{3}}\arctan {\frac {\sqrt {3}}{9}}}\right)}{3}}\right)\\&\simeq 15.3345a^{2}\end{aligned}}}

a is the length of one of its sides.

## Dissection

Coxeter states that every parallel-sided 2m-gon can be divided into m(m-1)/2 rhombs. For the regular tetradecagon, m=7, and it can be divided into 21: 3 sets of 7 rhombs. This decomposition is based on a Petrie polygon projection of a 7-cube, with 21 of 672 faces. [1] The list A006245 defines the number of solutions as 24698, including up to 14-fold rotations and chiral forms in reflection.

## Numismatic use

The regular tetradecagon is used as the shape of some commemorative gold and silver Malaysian coins, the number of sides representing the 14 states of the Malaysian Federation.[2]

## References

1. Coxeter, Mathematical recreations and Essays, Thirteenth edition, p.141
2. The Numismatist, Volume 96, Issues 7-12, Page 1409, American Numismatic Association, 1983.