barycentricSubdivision(D,R)
If $\Delta$ is an abstract simplicial complex, the barycentric subdivision of $\Delta$ is the abstract simplicial complex whose ground set (vertices) is the set of faces of $D$ and whose faces correspond to sequences $\{(F_0, F_1, \ldots, F_k)\}$ where $F_i$ is an $i$-dimensional face containing $F_{i-1}$. In order to understand how the data of the barycentric subdivision is organized, we work through a simple example.
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To make sense of the facets of the barycentric subdivision, we order the faces of $\Delta$ as follows.
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The indices of the variables appearing in each monomial (or facet) $F$ in the facets of $\Gamma$ determines a sequence of monomials (faces) in $\Delta$.
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