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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.)
Software:
TOPCOM
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References:
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