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Regular dodecagon | |||
---|---|---|---|

Edges and vertices | 12 | ||

Schläfli symbols | {12} t{6} | ||

Coxeter–Dynkin diagrams | >- | Symmetry group | Dihedral (D_{12}) |

Area (with t=edge length) | $A\; =\; 3\; cotleft(frac\{pi\}\{12\}\; right)\; t^2$ $=\; 3\; left(2+sqrt\{3\}\; right)\; t^2$ $simeq\; 11.19615242\; t^2.$ | ||

Internal angle (degrees) | 150° |

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:

- $$

& simeq 11.19615242,a^2.end{align}

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

- $A\; =\; 6\; sinleft(frac\{pi\}\{6\}right)\; R^2\; =\; 3\; R^2.$

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

- $$

& simeq 3.2153903,r^2.end{align}

Here are 3 example periodic plane tilings that use dodecagons:

Semiregular tiling 3.12.12 | Semiregular tiling: 4.6.12 | A demiregular tiling: 3.3.4.12 & 3.3.3.3.3.3 |

- When spelled uppercase, the outlines of the letters E and H (and I in a slab serif font) are all dodecagons.
- The Australian 50-cent coin, Fijian 50-cent, Tongan 50-seniti, and Solomon Island 50-cent coin are regular dodecagons. Croatian 25 kuna coin has a dodecagonal shape as well. Until July 2005, a Romanian coin (5000 ROL) was also dodecagonal. The Canadian penny was dodecagonal from 1982 to 1996 as well as the South Vietnamese 20 Ðong coin until 1975. Zambian 50 ngwee (until 1992) and Malawian 50 tambala (until 1995) coins were dodecagonal. The Mexican 20 cent coin is also 12-sided.

- dodecagonal number
- Dodecahedron - a regular polyhedron with 12 pentagonal faces.
- The E6 polytope can be drawn with an orthogonal projection inside a regular dodecagon.

- 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
- Definition and properties of a dodecagon With interactive animation

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Last updated on Monday August 04, 2008 at 12:26:37 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Monday August 04, 2008 at 12:26:37 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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