# Dodecagons - polygons with 12 sides

Categories: gcse geometry

A dodecagon is a flat shape with 12 straight sides.

## Regular and irregular dodecagons

A *regular dodecagon* is a 12-sided shape where every side is the same length and every corner has the same angle. All regular dodecagons have the same shape, like this:

An *irregular dodecagon* is a 12 sides shape where not every side and angle are equal. There are many different irregular dodecagon shapes, here is an example:

## Name

The name *dodecagon* is a combination of the words *dodeca* (Greek meaning *twelve*) and *gonia* (Greek meaning *corner*).

Dodecagons are sometimes called *12-gons*.

## Interior angles

The interior angles of a dodecagon are shown here:

The sum of these 12 angles is given by the formula:

```
sum of interior angles = (n - 2) x 180
```

Where *n* is the number of sides. In this case, the number of sides *n* is 12, so the sum of the interior angles is:

```
(12 - 2) x 180 = 1800 degrees
```

For a regular dodecagon, all the interior angles are equal:

This means that the interior angle of a regular dodecagon is:

```
1800 / 12 = 150 degrees
```

## Exterior angles

The exterior angles of a dodecagon are shown here:

The sum of the exterior angles of *any polygon* is 360 degrees.

For a regular dodecagon, all the interior angles are equal:

This means that the exterior angle of a regular dodecagon is:

```
360 / 12 = 30 degrees
```

## Symmetry of regular dodecagons

A regular dodecagon has 12 lines of symmetry. This means that it can be reflected over each of the 12 grey lines shown here:

A regular dodecagon has rotational symmetry of order 12. This means that if it rotated about its centre by a 12th of a full turn, it will map onto itself:

## Real life examples

A number of coins around the world are regular dodecagons, including the British pound.

## See also

- Regular polygons
- Interior and exterior angles of a polygon
- Triangles
- Quadrilaterals
- Quadrilateral family tree
- Pentagons - polygons with 5 sides
- Hexagons - polygons with 6 sides
- Heptagons - polygons with 7 sides
- Octagons - polygons with 8 sides
- Nonagons - polygons with 9 sides
- Decagons - polygons with 10 sides
- Hendecagons - polygons with 11 sides
- n-gons - polygons with any number of sides
- Other types of polygon
- Star polygons

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