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are called ridges. The faces of P may be partially ordered by inclusion, forming a face lattice that has as its top element P itself and as its bottom element the empty set.

A key tool in polyhedral combinatorics is the f-vector of a polytope, the vector (f₀, f₁, ..., f_d − 1) where f_i is the number of i-dimensional features of the polytope. For instance,

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