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Displaying similar documents to “Vector spaces spanned by the angle sums of polytopes.”

Rigidity and flexibility of virtual polytopes

G. Panina (2003)

Open Mathematics

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All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.

Riemann sums over polytopes

Victor Guillemin, Shlomo Sternberg (2007)

Annales de l’institut Fourier

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It is well-known that the N -th Riemann sum of a compactly supported function on the real line converges to the Riemann integral at a much faster rate than the standard O ( 1 / N ) rate of convergence if the sum is over the lattice, Z / N . In this paper we prove an n-dimensional version of this result for Riemann sums over polytopes.

The number of vertices of a Fano polytope

Cinzia Casagrande (2006)

Annales de l’institut Fourier

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Let X be a Gorenstein, ℚ -factorial, toric Fano variety. We prove two conjectures on the maximal Picard number of X in terms of its dimension and its pseudo-index, and characterize the boundary cases. Equivalently, we determine the maximal number of vertices of a simplicial reflexive polytope.