In geometry, ellipsoid 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[1] and
a square-triangle crystal containing 24 ellipsoids[2] 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.
| |
---|---|
Abstract packing |
|
Circle packing |
|
Sphere packing |
|
Other 2-D packing |
|
Other 3-D packing |
|
Puzzles |
|