Research Article

Space-filling zonotopes

G. C. Shepharda1

a1 University of East Anglia, Norwich NR4 7TJ, England.

By a zonotope we mean any set in Euclidean n-dimensional space Rn which can be written as a Minkowski (vector) sum of a finite number of line segments. A zonotope is a convex centrally-symmetric polytope, and all its faces are zonotopes. Familiar examples of three-dimensional zonotopes include the cube, rhombic dodecahedron, elongated dodecahedron (Figure 1) and truncated octahedron. Photographs of models of more complicated examples appear in [1, Plate II].

(Received May 03 1974)

Key Words:

  • 10E30: NUMBER THEORY; Geometry of numbers; Lattice packing and coverin;
  • 5OB3O: GEOMETRY; Euclidean geometry; Divsion of space;
  • 52A25: CONVEX SETS; Convex polyhedra;
  • 52A45: CONVEX SETS; Packing and covering