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In geometry, a dodecagon is any 12-sided polygon or 12-gon. ==Regular dodecagon== A ''regular dodecagon'' has Schläfli symbol and can be constructed as a truncated hexagon, t, or a twice-truncated triangle, tt. It has all sides of equal length and all angles equal to 150°. It has 12 lines of symmetry and rotational symmetry of order 12. Its Schläfli symbol is . The area of a regular dodecagon with side ''a'' is given by: : Or, if ''R'' is the radius of the circumscribed circle,〔See also Kürschák's geometric proof on (the Wolfram Demonstration Project )〕 : And, if ''r'' is the radius of the inscribed circle, : A simple formula for area (given the two measurements) is: where ''d'' is the distance between parallel sides. Length ''d'' is the height of the dodecagon when it sits on a side as base, and the diameter of the inscribed circle. By simple trigonometry, . The perimeter for an inscribed dodecagon of radius 1 is 12√(2 - √3), or approximately 6.21165708246. 〔''Plane Geometry: Experiment, Classification, Discovery, Application'' by Clarence Addison Willis B., (1922) Blakiston's Son & Company, p. 249 ()〕 The perimeter for a circumscribed dodecagon of radius 1 is 24(2 – √3), or approximately 6.43078061835. Interestingly, this is double the value of the area of the ''inscribed'' dodecagon of radius 1. 〔''Elements of geometry'' by John Playfair, William Wallace, John Davidsons, (1814) Bell & Bradfute, p. 243 ()〕 With respect to the above-listed equations for area and perimeter, when the radius of the inscribed dodecagon is 1, note that the area of the inscribed dodecagon is 12(2 – √3) and the ''perimeter'' of this same inscribed dodecagon is 12√(2 - √3). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「dodecagon」の詳細全文を読む スポンサード リンク
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