Let each sphere in a sphere packing expand uniformly until it touches its neighbors on flat faces. Call the resulting polyhedron the local cell. Then the local density is given by
When the local cell is a regular dodecahedron, then
Let each sphere in a sphere packing expand uniformly until it touches its neighbors on flat faces. Call the resulting polyhedron the local cell. Then the local density is given by
When the local cell is a regular dodecahedron, then
Weisstein, Eric W. "Local Density." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LocalDensity.html