Dodecagon
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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 \cot \frac = 3 a^2 \left( 2+\sqrt \right) \simeq 11.1962 a^2.]
Alternately, [A = 3 r^2 \frac] where r is the radius of a circumscribed circle.
Dodecagon construction
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
- 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
External links
- [Dodecagon and Kurschak's Tile and Theorem] by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
- , [Dodecagon] at MathWorld.
Polygons Triangle | Quadrilateral | Pentagon | Hexagon | Heptagon | Octagon | Enneagon (Nonagon) | Decagon | Hendecagon | Dodecagon | Triskaidecagon | Pentadecagon | Heptadecagon | Enneadecagon | Icosagon | Tricontagon | Pentacontagon | Hectagon | Chiliagon | Myriagon
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