Characterizing Graphs of Zonohedra

Details Characterizing Graphs of Zonohedra Characterizing Graphs of Zonohedra

2008-11-03

arxiv.org/abs/0811.0254v1

Computer Science

Computational Geometry

13 pages, 5 figures

Scientific paper

A classic theorem by Steinitz states that a graph G is realizable by a convex polyhedron if and only if G is 3-connected planar. Zonohedra are an important subclass of convex polyhedra having the property that the faces of a zonohedron are parallelograms and are in parallel pairs. In this paper we give characterization of graphs of zonohedra. We also give a linear time algorithm to recognize such a graph. In our quest for finding the algorithm, we prove that in a zonohedron P both the number of zones and the number of faces in each zone is O(square root{n}), where n is the number of vertices of P.

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