In geometry,
ellipsoid
An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.
An ellipsoid is a quadric surface; that is, a surface that may be defined as the ...
packing is the problem of arranging identical ellipsoid throughout three-dimensional space to fill the maximum possible fraction of space.
The currently densest known packing structure for ellipsoid has two candidates,
a simple monoclinic crystal with two ellipsoids of different orientations and
a square-triangle crystal containing 24 ellipsoids
in the fundamental cell. The former monoclinic structure can reach a maximum packing fraction around
for ellipsoids with maximal aspect ratios larger than
. The packing fraction of the square-triangle crystal exceeds that of the monoclinic crystal for specific biaxial ellipsoids, like ellipsoids with ratios of the axes
and
. Any ellipsoids with aspect ratios larger than one can pack denser than spheres.
See also
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Packing problems
Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few cont ...
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Sphere packing
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three- dimensional Euclidean space. However, sphere pack ...
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Tetrahedron packing In geometry, tetrahedron packing is the problem of arranging identical regular tetrahedra throughout three-dimensional space so as to fill the maximum possible fraction of space.
Currently, the best lower bound achieved on the optimal packing fr ...
References
{{Packing problems
Packing problems