Here is one way to pack pennies on a plane. $($Imagine the pattern covers the plane infinitely in all directions.$)$

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a$.$ Think of the center of each penny as a convenience store. Draw the corresponding Voronoi diagram on top of the pennies.

This gives new meaning to the "give a penny" pile.

b$.$ What do you notice about the polygons formed, relative to the pennies?

c$.$ Calculate the percentage of the plane covered by pennies.