Dodecagons - polygons with 12 sides

By Martin McBride, 2022-10-10
Tags: dodecagon 12 sided shape regular polygon irregular polygon
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:

Regular dodecagon

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:

Irregular dodecagon

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:

Interior angles of a dodecagon

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:

Interior angles of an irregular dodecagon

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:

Exterior angles of a dodecagon

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

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

Exterior angles of an irregular dodecagon

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:

Lines of symmetry of a regular nonangon

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:

Lines of symmetry of a regular dodecagon

Real life examples

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

See also



Join the GraphicMaths Newletter

Sign up using this form to receive an email when new content is added:

Popular tags

adder adjacency matrix alu and gate angle area argand diagram binary maths cartesian equation chain rule chord circle cofactor combinations complex modulus complex polygon complex power complex root cosh cosine cosine rule cpu cube decagon demorgans law derivative determinant diagonal directrix dodecagon eigenvalue eigenvector ellipse equilateral triangle eulers formula exponent exponential exterior angle first principles flip-flop focus gabriels horn gradient graph hendecagon heptagon hexagon horizontal hyperbola hyperbolic function hyperbolic functions infinity integration by parts integration by substitution interior angle inverse hyperbolic function inverse matrix irregular polygon isosceles trapezium isosceles triangle kite koch curve l system line integral locus maclaurin series major axis matrix matrix algebra mean minor axis nand gate newton raphson method nonagon nor gate normal normal distribution not gate octagon or gate parabola parallelogram parametric equation pentagon perimeter permutations polar coordinates polynomial power probability probability distribution product rule pythagoras proof quadrilateral radians radius rectangle regular polygon rhombus root set set-reset flip-flop sine sine rule sinh sloping lines solving equations solving triangles square standard curves standard deviation star polygon statistics straight line graphs surface of revolution symmetry tangent tanh transformation transformations trapezium triangle turtle graphics variance vertical volume of revolution xnor gate xor gate