Xanthir wrote:The original problem statement only gives you a collection of points, with no pathing information. There is no way to distinguish a 5-star from a pentagon.

Pathing information honestly makes this easier, as that functions as a free sorting of the points, allowing you to go with daydalus' original algorithm.

Generally, though, I believe an n-gon is assumed to be a planar graph, giving you only one interpretation of 'regular n-gon'.

*nod*

Hmm. could you consider something with a "saw-tooth" pattern, going up and down in the z-axis, as being a regular n-gon. (same angle between any 3 adjacent sides, same distance)

And if [imath](e^a)^k[/imath] = 1 for k!=0 then, I think, the least z>0 such that [imath](e^a)^b = (e^z)[/imath] will also generate the points in question... right? God damn it, my group theory is rusty.