Kids Encyclopedia Facts
Type Regular polygon
Edges and vertices 14
Schläfli symbol {14}, t{7}
Coxeter diagram
Symmetry group Dihedral (D14), order 2×14
Internal angle (degrees) ≈154.2857°
Dual polygon Self
Properties Convex, 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

\begin{align}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{align}

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. 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.

## Images for kids

Tetradecagon Facts for Kids. Kiddle Encyclopedia.