A k-dimensional subspace stabs a polytope exactly when the Chow forms of a suitable face obey a fixed sign pattern.
Dalbec, and B Sturmfels: Introduction to Chow forms , Invariant Methods in Discrete and Computational Geometry: Proceedings of the Curac ¸ao Conference, 13–17 June, 1994 (1995)
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How to stab a polytope
A k-dimensional subspace stabs a polytope exactly when the Chow forms of a suitable face obey a fixed sign pattern.