List of shapes with known packing constant

The packing constant of a geometric body is the largest average density achieved by packing arrangements of congruent copies of the body.

For most bodies the value of the packing constant is unknown.

[1] The following is a list of bodies in Euclidean spaces whose packing constant is known.

[1] Fejes Tóth 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.

In addition to these bodies, the packing constants of hyperspheres in 8 and 24 dimensions are almost exactly known.