For a given point lattice, some number of points will be within distance of the origin. A Waterman polyhedron
is the convex hull of these points. A progression
of Waterman polyhedra with increasing within the cubic lattice
is illustrated above. A progression based on the lattice of the diamond structure
has been illustrated by Bourke (2002).
Bourke, P. "Waterman Polyhedra." Dec. 2002. http://astronomy.swin.edu.au/~pbourke/geometry/waterman/.Darcas,
G. (Ed.). "Polyhedra 2, Part 1." In Symmetry: Culture and Science, Vol. 13.
Budapest, Hungary: Symmetrion, pp. 129-171.
of the origin. A Waterman polyhedron
is the convex hull of these points. A progression
of Waterman polyhedra with increasing 
within the cubic lattice
is illustrated above. A progression based on the lattice of the diamond structure
has been illustrated by Bourke (2002).
