I want to tile the plane with equal-sized regular polygons of $n$ sides.

Obviously for some $n$, the tiles will be able to tessellate and cover the whole plane (e.g triangles, squares, hexagons)

I just want to know the maximum percentage of the plane that can be covered for each $n$.

What happens when $n$ approaches infinity? I know the shape will tend to a circle, which has a known optimal packing, but is there a general pattern to it?


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