The
packing constant of a geometric body is the largest average density achieved by packing arrangements of
congruent
Congruence may refer to:
Mathematics
* Congruence (geometry), being the same size and shape
* Congruence or congruence relation, in abstract algebra, an equivalence relation on an algebraic structure that is compatible with the structure
* In modu ...
copies of the body. For most bodies the value of the packing constant is unknown.
The following is a list of bodies in Euclidean spaces whose packing constant is known.
proved that in the plane, a
point symmetric body has a packing constant that is equal to its
translative packing constant and its
lattice packing constant.
Therefore, any such body for which the lattice packing constant was previously known, such as any
ellipse
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...
, consequently has a known packing constant. In addition to these bodies, the packing constants of
hyperspheres in 8 and 24 dimensions are almost exactly known.
References
{{DEFAULTSORT:Shapes with known packing constant
Packing problems
Discrete geometry
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