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Given a subspace Formula: see text and a finite set S⊆ℝ d , we introduce the Delaunay complex, Formula: see text, restricted by Formula: see text. Its simplices are spanned by subsets T⊆S for which the common intersection of Voronoi cells meets Formula: see text in a non-empty set. By the nerve theorem, Formula: see text and Formula: see text are homotopy equivalent if all such sets are contractible. This paper proves a sufficient condition for Formula: see text and Formula: see text be homeomorphic.
Edelsbrunner et al. (Fri,) studied this question.