Question

suppose you have tile that are all the same size and the same shape, with the shapes being a regular polygon with n sides. when you tile the plane with these tiles there are no gaps and no overlaps. assume that m tiles meet in a corner.
a) prove that m(n-2) = 2n
b) prove that n-2 <= (2/3)n
c) prove that n<= 6
d) explain why the only regular polygons that can tile a plane are triangles squares or hexagons