Tetradecagon

In geometry, a tetradecagon or tetrakaidecagon or 14-gon is a fourteen-sided polygon. Shapes like this are studied to understand how angles and lines work together. A regular tetradecagon has all sides and angles equal, making it a special and symmetrical shape.

Tetradecagons can be found in art, architecture, and nature. Sometimes they appear in designs or patterns where symmetry is important. Learning about tetradecagons helps us explore the beauty and order in geometric shapes.

Understanding tetradecagons also helps in many fields, such as math, engineering, and even computer graphics. It shows how shapes with many sides can have interesting properties and uses.

Regular tetradecagon

A regular tetradecagon is a fourteen-sided polygon with all sides and angles equal. It has a Schläfli symbol of {14} and can be thought of as a truncated heptagon.

The area of a regular tetradecagon can be calculated if you know the length of one side, called a. The formula is complex, but it tells us the area is roughly 15.3345 times a squared.

Construction

Because 14 equals 2 times 7, a regular tetradecagon cannot be created using just a compass and straightedge. However, it can be constructed using special tools like neusis or an angle trisector.

Symmetry

The regular tetradecagon has a special kind of balance called Dih₁₄ symmetry, which means it looks the same after certain turns and flips. It has 28 different ways to match up its shape perfectly.

There are also simpler patterns of balance called cyclic symmetries, like Z₁₄, Z₇, Z₂, and Z₁. These help us understand how the shape can change a little while still keeping some of its balanced look. Two special irregular tetradecagons, d14 and p14, have their own unique balances and are linked to each other in a special way called being duals.

Dissection

A regular tetradecagon, which has fourteen sides, can be divided into smaller shapes called rhombi. Specifically, it can be split into 21 rhombi, arranged in 3 groups of 7. This way of dividing the shape comes from a special view of a seven-dimensional shape called a 7-cube. There are many different ways to arrange these rhombi, with a total of 24,698 possible patterns when you consider rotations and reflections.

Main article: Zonogon
Regular polygons
Petrie polygon
7-cube
OEIS

Numismatic use

The regular tetradecagon is used as the shape of some special gold and silver Malaysian coins. The 14 sides of these coins stand for the 14 states in the Malaysian Federation.

Related figures

A tetradecagram is a 14-sided star polygon, represented by the symbol {14/n}. There are two regular star polygons: {14/3} and {14/5}. These shapes use the same points but connect every third or fifth point to form a star.

One famous use of a fourteen-pointed star is in the flag of Malaysia, where a yellow {14/6} tetradecagram appears in the top-right corner. This symbol stands for the unity of the thirteen states and the federal government.

Different ways to change a seven-sided shape can create many interesting tetradecagram forms with evenly spaced points and two different line lengths.