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triacontagon : ウィキペディア英語版
triacontagon

In geometry, a triacontagon is a thirty-sided polygon or 30-gon. The sum of any triacontagon's interior angles is 5040 degrees.
==Regular triacontagon ==

The ''regular triacontagon'' is a constructible polygon, by an edge-bisection of a regular pentadecagon, and can also be constructed as a truncated pentadecagon, t.
One interior angle in a regular triacontagon is 168°, meaning that one exterior angle would be 12°. The triacontagon is the largest regular polygon whose interior angle is the sum of the interior angles of smaller polygons: 168° is the sum of the interior angles of the equilateral triangle (60°) and the regular pentagon (108°).
The area of a regular triacontagon is (with )
:A = \frac t^2 \cot \frac = \frac t^2 (\sqrt)}} = \frac t^2 (\sqrt + 3\sqrt + \sqrt\sqrt t \cot \frac = \frac t(\sqrt + 3\sqrt + \sqrt\sqrt t \csc \frac = \frac t(2 + \sqrt + \sqrt{15+6\sqrt{5}})

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