# Characterizing Graphs of Zonohedra - Computer Science > Computational Geometry

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Abstract: A classic theorem by Steinitz states that a graph G is realizable by a convexpolyhedron if and only if G is 3-connected planar. Zonohedra are an importantsubclass of convex polyhedra having the property that the faces of a zonohedronare parallelograms and are in parallel pairs. In this paper we givecharacterization of graphs of zonohedra. We also give a linear time algorithmto recognize such a graph. In our quest for finding the algorithm, we provethat in a zonohedron P both the number of zones and the number of faces in eachzone is Osquare root{n}, where n is the number of vertices of P.

Author: ** Muhammad Abdullah Adnan, Masud Hasan**

Source: https://arxiv.org/