Reconstructing a Simple Polytope from its Graph
Hans Achatz, Peter Kleinschmidt · Birkhäuser Basel eBooks · 2000
Let P be a simple polytope with dimension d and G(P) its edge graph. It has been shown in [ BlM87 ] and [ Kal88 ] that G(P) already determines the complete face-lattice of P . However, the constructive approach used in [ Kal88 ] requires the computation of all orderings in vert( P )1 which is computationally prohibitive for polytopes of even very small sizes. In this paper we propose an algorithm which is still exponential but does work with reasonable computing time for non-trivial simple polytopes.