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

In geometry, a heptacontagon (or hebdomecontagon from Ancient Greek ἑβδομήκοντα, seventy〔(Greek Numbers and Numerals (Ancient and Modern) ) by Harry Foundalis〕) is a seventy-sided polygon or 70-gon.〔.〕〔(''The New Elements of Mathematics: Algebra and Geometry ) by Charles Sanders Peirce (1976), p.298〕 The sum of any heptacontagon's interior angles is 12240 degrees.
A ''regular heptacontagon'' is represented by Schläfli symbol and can also be constructed as a truncated triacontapentagon, t, which alternates two types of edges.

==Regular heptacontagon properties==
One interior angle in a regular heptacontagon is 174°, meaning that one exterior angle would be 5°.
The area of a regular heptacontagon is (with )
:A = \fract^2 \cot \frac
and its inradius is
:r = \fract \cot \frac
The circumradius of a regular heptacontagon is
:R = \fract \csc \frac
Since 70 = 2 × 5 × 7, a regular heptacontagon 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〕

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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