In geometry, a dodecagon is any polygon with twelve sides and twelve angles.

It usually refers to a regular dodecagon, having all sides of equal length and all angles equal to 150°. Its Schläfli symbol is {12}.

The area of a regular dodecagon with side a is given by:

Or, if R is the radius of the circumscribed circle,

And, if r is the radius of the inscribed circle,

A simple formula for area (given the two measurements) is: Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle A\,=\,3ad

Length d is the height of the dodecahedron when it sits on a side as base, and the diameter of the inscribed circle.

By simple trigonometry, Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle d\,=\,a(1\,+\,2cos{30^\circ}\,+\,2cos{60^\circ}) .

A regular dodecagon can fill a plane vertex with other regular polygons:

A regular dodecagon is constructible using compass and straightedge:

Construction of a regular dodecagon

Here are 3 example periodic plane tilings that use dodecagons: