George W. Hart
george@li.net
http://www.georgehart.com/

An efficient algorithm is presented to construct arbitrary zonohedra and to "zonohedrify" a given polyhedron. There are relatively few interesting processes which input an arbitrary polyhedron and output a related polyhedron. Well-known examples are truncation, stellation, dualization (reciprocation in a sphere), and compounding. To this list can be added zonohedrification, in which the vertex directions of the original polyhedron (relative to an arbitrary center) determine the edge directions of the resulting zonohedrification. To give the reader insight into zonohedral structure and an understanding of the algorithm, a few mathematical properties of zonohedra are outlined.