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A honeycomb-like packing that forms hexagons.

Given n circles and a perimeter p, the total area of the convex hull is A_(Convex Hull)=2sqrt(3)(n-1)+p(1-1/2sqrt(3))+pi(sqrt(3)-1). Furthermore, the actual area equals this ...

Finding the densest not necessarily periodic sphere packing.

An a×b rectangle can be packed with 1×n strips iff n|a or n|b.

The polyhedron resulting from letting each sphere in a sphere packing expand uniformly until it touches its neighbors on flat faces.

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 ...

The fraction eta of a volume filled by a given collection of solids.

Maximize the amount of floor space which can be covered with a fixed tile (Hoffman 1998, p. 173).

A parallelogram (parallelepiped) containing the minimum repeatable elements of a circle (sphere) packing.

A box can be packed with a harmonic brick a×ab×abc iff the box has dimensions ap×abq×abcr for some natural numbers p, q, r (i.e., the box is a multiple of the brick).