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?