Waterman polyhedron

With each point of 3D space we can associate a family of Waterman polyhedra with different values of radii of the circumscribed spheres.

[citation needed] Generalized Waterman polyhedra are defined as the convex hull derived from the point set of any spherical extraction from a regular lattice.

[citation needed] Each of the 10 lattices were examined to isolate those particular origin points that manifested a unique polyhedron, as well as possessing some minimal symmetry requirement.

[citation needed] From a viable origin point, within a lattice, there exists an unlimited series of polyhedra.

[citation needed] Given its proper sweep interval, then there is a one-to-one correspondence between each integer value and a generalized Waterman polyhedron.