In geometry, a dodecagon is a polygon with exactly twelve sides. When spelled uppercase, the outlines of the letters E and H (and I in a slab serif font) are all dodecagons.

A regular dodecagon is a dodecagon with all sides having equal length and all interior angles having the same size of 150 degrees. The area of a regular decagon is given by: $A\; =\; 3\; a^2\; \backslash cot\; \backslash frac\{\backslash pi\}\{12\}\; =\; 3\; a^2\; \backslash left(\; 2+\backslash sqrt\{3\}\; \backslash right)\; \backslash simeq\; 11.1962\; a^2.$

Alternately, $A\; =\; 3\; r^2\; \backslash frac\{\}\{\}$ where r is the radius of a circumscribed circle.

Dodecagon construction

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A regular dodecagon is constructible with compass and straightedge. The following is a 23 step animation illustrating one way it can be done. Notice that the compass radius is unaltered during steps 8 through 11.

Dodecagons in real life

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• The Australian 50-cent coin is 12-sided. Until July 2005, a Romanian coin (5000 ROL) was also dodecagonal. The Canadian penny was dodecagonal from 1982 to 1996.

See also

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• dodecagonal number

External links

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• Dodecagon and Kurschak's Tile and Theorem by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
• Kürschak's Tile and Theorem

Polygons

დოდეკაგონი | Dodecágono | 十二边形