
Packing Pennies in the Plane 
Suppose we now look at a cell in a layout. Draw the circumscribing circle as well, or at least its intersection with the cell. Where it extends beyond the cell, the line cut off by the cell boundary will be the bisector of the rhombus associated to two discs whose hexagonally circumscribed circles intersect.
We can now divide up the cell into distinct regions of three types:






The density of the distribution in the first type of region is
of course 