A face poset is a partially ordered set (poset) that organizes the faces of a convex polytope or more generally, a simplicial complex based on inclusion. Each face corresponds to a subset of vertices, and the order is defined by inclusion, meaning that one face is considered less than or equal to another if it is contained within the other. This structure is crucial for studying the combinatorial properties of polytopes, as well as their associated algebraic invariants.
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