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I have a set of points on the plane (300 000 points). How do I find a polygon with equal cosines of angles and equal sides where vertices of polygon are some of points? The more number of sides and more lengths of sides the better.

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How is your set of points given? –  Henning Makholm Oct 15 '11 at 19:48
    
It is random sequence of points from file –  dmak9 Oct 15 '11 at 19:52
    
That doesn't answer how they are given. As coordinates? Rectangular? Are the coordinates always rational? –  Henning Makholm Oct 15 '11 at 19:57
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Are the coordinates always rational? If so, I don't think you'll be able to create other regular polygons than squares, which will be fairly easy to check. –  Henning Makholm Oct 15 '11 at 20:09
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In support of Henning's comment, it is shown that the only regular lattice polygon is a square at web.me.com/paulscott.info/lattice-points/5regular.html#anchor2 –  Gerry Myerson Oct 15 '11 at 22:38
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