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http://discovermagazine.com/2016/janfeb/55-pentagon-puzzler

This raises the question...can any polygon with n sides be manipulated so that it will tile with other similar polygons? Can one find a shape of a 20 sided polygon that will tile with the same shaped 20 sided polygon, or a 53 sided polygon?

More to the point...is there any intuitive proof one way or the other?

tex