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

In geometry, an enneacontagon or enenecontagon (from Ancient Greek ἑννενήκοντα, ninety〔(Greek Numbers and Numerals (Ancient and Modern) ) by Harry Foundalis〕) is a ninety-sided polygon or 90-gon.〔.〕〔(''The New Elements of Mathematics: Algebra and Geometry ) by Charles Sanders Peirce (1976), p.298〕 The sum of any enneacontagon's interior angles is 15840 degrees.
A ''regular enneacontagon'' is represented by Schläfli symbol and can be constructed as a truncated tetracontapentagon, t, which alternates two types of edges.
==Regular enneacontagon properties==
One interior angle in a regular enneacontagon is 176°, meaning that one exterior angle would be 4°.
The area of a regular enneacontagon is (with )
:A = \fract^2 \cot \frac
and its inradius is
:r = \fract \cot \frac
The circumradius of a regular enneacontagon is
:R = \fract \csc \frac
Since 90 = 2 × 32 × 5, a regular enneacontagon is not constructible using a compass and straightedge,〔(Constructible Polygon )〕 but is constructible if the use of an angle trisector is allowed.〔http://www.math.iastate.edu/thesisarchive/MSM/EekhoffMSMSS07.pdf〕

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