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Webs of stars or how to triangulate free sums of point configurations. (English) Zbl 1416.52016
If $$P\subseteq\mathbb{R}^d$$ and $$Q\subseteq\mathbb{R}^e$$ are finite point sets containing the origin as a point that lies in the interior of the convex hull, the free sum $$P\oplus Q$$ of $$P$$ and $$Q$$ is the finite point set in $$\mathbb{R}^{d+e}$$ defined as the union of $$P\times\{0\}$$ and $$\{0\}\times Q$$. The paper classifies the triangulations of free sums $$P\oplus Q$$ in terms of the triangulations of the summands $$P$$ and $$Q$$. As a case study, the methods are applied to triangulations of point sets associated with the vertex-sets of smooth Fano polytopes.
##### MSC:
 52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry) 52B45 Dissections and valuations (Hilbert’s third problem, etc.) 52B12 Special polytopes (linear programming, centrally symmetric, etc.)
##### Keywords:
point configuration; triangulation; free sum; Fano polytope
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##### References:
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