Tetradecagon

In geometry, a tetradecagon or tetrakaidecagon or 14-gon is a fourteen-sided polygon.

Shapes like this help us learn how angles and lines fit together. A regular tetradecagon has all sides and angles the same, making it a neat and balanced shape.

Tetradecagons appear in art, buildings, and nature. They show up in designs where balance and symmetry matter. Learning about tetradecagons helps us see the beauty and order in shapes.

Studying tetradecagons is useful in many areas, like math, building design, and computer graphics. It shows how shapes with many sides can have special traits and uses.

Regular tetradecagon

A regular tetradecagon is a shape with fourteen sides that are all the same length and all angles the same. It has a Schläfli symbol of {14} and can be thought of as a truncated heptagon.

The area of a regular tetradecagon can be found if you know the length of one side, called a. The formula is a bit complicated, but it shows the area is about 15.3345 times a squared.

Construction

Because 14 is 2 times 7, a regular tetradecagon cannot be made using just a compass and straightedge. But it can be made using special tools like neusis or an angle trisector.

Symmetry

The regular tetradecagon has a special balance called Dih₁₄ symmetry. This means it looks the same after turns and flips. It has 28 ways to match up perfectly.

There are also simpler balances called cyclic symmetries, like Z₁₄, Z₇, Z₂, and Z₁. These show how the shape can change a little but still keep some balance. Two special irregular tetradecagons, d14 and p14, have their own balances and are linked as duals.

Dissection

A regular tetradecagon has fourteen sides. It can be divided into smaller shapes called rhombi. It can be split into 21 rhombi, in 3 groups of 7. This comes from a view of a seven-dimensional shape called a 7-cube. There are many ways to arrange these rhombi.

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 represent the 14 states in the Malaysian Federation.

Related figures

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

A fourteen-pointed star is used in the flag of Malaysia. It appears in the top-right corner. This symbol shows the unity of the thirteen states and the federal government.

There are many ways to change a seven-sided shape to make different tetradecagram forms with evenly spaced points and two different line lengths.