Abstract
A simple cell complex C in Euclidean d -space E d is a covering of E d by finitely many convex j -dimensional polyhedra (the j -faces of C), each of which is in the closure of exactly d-j +1 d -faces of C . An algorithm that recognises when C is the projection of the set of faces bounding some convex polyhedron P ( C ) in E d+1 , and that constructs P ( C ) provided its existence is outlined. The method is optimal at least for d =2. No complexity results were previously known for both problems. The results have applications in statics, to the recognition of Voronoi diagrams, and to planar point-location,
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