Discrete & Computational Geometry

, Volume 2, Issue 1, pp 49–64 | Cite as

A criterion for the affine equivalence of cell complexes inR d and convex polyhedra inRd+1

  • Franz Aurenhammer


A criterion is given that decides, for a convex tilingC ofR d , whetherC is the projection of the faces in the boundary of some convex polyhedronP inRd+1. Its applicability is restricted neither by the properties nor by the dimension ofC. It turns out to be conceptually simpler than other criteria and allows the easy examination of various classes of cell complexes. In addition, the criterion is constructive, that is, it can be used to constructP provided it exists.


Simplicial Complex Voronoi Diagram Discrete Comput Geom Cell Complex Convex Polyhedron 
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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Franz Aurenhammer
    • 1
    • 2
  1. 1.Institutes for Information ProcessingTechnical University of GrazAustria
  2. 2.Austrian Computer SocietyGrazAustria

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