Testwiki:Reference desk/Archives/Mathematics/2016 May 11

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May 11

Maximum coverage of plane by identical regular polygons...

Looking for the maximum coverage of the plane by each regular identical N-polygon. For N=3,4,6 the answer is 1.00. For 8, I think it is the Truncated square tiling where the part covered = 2sqrt(2)-2. Any ideas on 5 ,7 and other numbers? The limit as N gets large is equal to the ${\eta }_h=\frac{\pi }{2\sqrt{3}}\approx 0.9069.$. Which is worst?Naraht (talk) 18:26, 11 May 2016 (UTC)

I suggest starting here and following the links backwards. (An earlier version of this post had a bunch of other links, but I think this is the best one and will answer most of your questions.) JBL (talk) 19:43, 11 May 2016 (UTC)