Displaying similar documents to “Uniform decompositions of polytopes”

Approximation of the Euclidean ball by polytopes

Monika Ludwig, Carsten Schütt, Elisabeth Werner (2006)

Studia Mathematica

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There is a constant c such that for every n ∈ ℕ, there is an Nₙ so that for every N≥ Nₙ there is a polytope P in ℝⁿ with N vertices and v o l ₙ ( B ₂ ⁿ △ P ) ≤ c v o l ₙ ( B ₂ ⁿ ) N - 2 / ( n - 1 ) where B₂ⁿ denotes the Euclidean unit ball of dimension n.

Delaunay polytopes derived from the Leech lattice

Mathieu Dutour Sikirić, Konstantin Rybnikov (2014)

Journal de Théorie des Nombres de Bordeaux

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A Delaunay polytope in a lattice L is perfect if any affine transformation that preserve its Delaunay property is a composite of an homothety and an isometry. Perfect Delaunay polytopes are rare in low dimension and here we consider the ones that one can get in lattice that are sections of the Leech lattice. By doing so we are able to find lattices with several orbits of perfect Delaunay polytopes. Also we exhibit Delaunay polytopes which remain Delaunay in some superlattices....

The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings

Birkett Huber, Jörg Rambau, Francisco Santos (2000)

Journal of the European Mathematical Society

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In 1994, Sturmfels gave a polyhedral version of the Cayley Trick of elimination theory: he established an order-preserving bijection between the posets of coherent mixed subdivisions of a Minkowski sum 𝒜 1 + ⋯ + 𝒜 r of point configurations and of coherent polyhedral subdivisions of the associated Cayley embedding 𝒞 ( 𝒜 1 , ⋯ , 𝒜 r ) . In this paper we extend this correspondence in a natural way to cover also non-coherent subdivisions. As an application, we show that the Cayley Trick combined with results of Santos...

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.