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The placement of objects so that they touch in some specified manner, often inside a container with specified properties. For example, one could consider a sphere packing, ...

A packing of polyhedron in three-dimensional space. A polyhedron which can pack with no holes or gaps is said to be a space-filling polyhedron. Betke and Henk (2000) present ...

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

A face-centered cubic sphere packing obtained by placing layers of spheres one on top of another. Because there are two distinct ways to place each layer on top of the ...

Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

A honeycomb-like packing that forms hexagons.

Find the minimum size square capable of bounding n equal squares arranged in any configuration. The first few cases are illustrated above (Friedman). The only packings which ...

Bezdek and Kuperberg (1991) have constructed packings of identical ellipsoids of densities arbitrarily close to ((24sqrt(2)-6sqrt(3)-2pi)pi)/(72)=0.753355... (OEIS A093824), ...

A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres ...

The best known packings of equilateral triangles into an equilateral triangle are illustrated above for the first few cases (Friedman). The best known packings of equilateral ...