The Baues conjecture in corank 3 (Q5952749)

For a collection \(A\) of vectors (points) in \(\mathbb R^n\), one may choose a collection of subsets of \(A\). If the collection covers \(A\) and has certain nice properties, specifically that for any two subsets \(C_1\), \(C_2\) in the collection, NEWLINENEWLINENEWLINE\(\star\) the intersections of the positive spans of \(C_1\) and \(C_2\) equals the positive span of the intersection of \(C_1\) and \(C_2\), and NEWLINENEWLINENEWLINE\(\star\) the linear span of \(C_1 \cap C_2\) meets \(C_1\) and \(C_2\) at the same set of points,NEWLINENEWLINENEWLINEit is called a polyhedral subdivision of \(A\) (where the ``positive span'' of a set of vectors is the set of linear combinations with non-negative coefficients). The two properties stated mean that a polyhedral subdivision is somewhat like a polytope.