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

In geometry, a pentacontagon or pentecontagon is a fifty-sided polygon or 50-gon.〔.〕〔(''The New Elements of Mathematics: Algebra and Geometry ) by Charles Sanders Peirce (1976), p.298〕 The sum of any pentacontagon's interior angles is 8640 degrees.
A ''regular pentacontagon'' is represented by Schläfli symbol and can be constructed as a quasiregular truncated icosipentagon, t, which alternates two types of edges.
==Regular pentacontagon properties==
One interior angle in a regular pentacontagon is 172.8°, meaning that one exterior angle would be 7.2°.
The area of a regular pentacontagon is (with )
:A = \fract^2 \cot \frac
and its inradius is
:r = \fract \cot \frac
The circumradius of a regular pentacontagon is
:R = \fract \csc \frac
Since 50 = 2 × 52, a regular pentacontagon is not constructible using a compass and straightedge,〔(Constructible Polygon )〕 and is not constructible even 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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