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

In geometry, a tetracontadigon (or tetracontakaidigon) is a forty-two-sided polygon, or ''42''-gon. (In Greek, the prefix tetraconta- means 40 and di- means 2.) The sum of any tetracontadigon's interior angles is 7200 degrees.
==Regular tetracontadigon==
The ''regular tetracontadigon'' can be constructed as a truncated icosihenagon, t.
One interior angle in a regular tetracontadigon is 171°, meaning that one exterior angle would be 8°.
The area of a regular tetracontadigon is (with )
:A = 10.5t^2 \cot \frac
and its inradius is
:r = \fract \cot \frac
The circumradius of a regular tetracontadigon is
:R = \fract \csc \frac
Since 42 = 2 × 3 × 7, a regular tetracontadigon 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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