Displaying similar documents to “Drawing 3-polytopes with good vertex resolution.”

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Badent, Melanie, Brandes, Ulrik, Cornelsen, Sabine (2011)

Journal of Graph Algorithms and Applications

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Alexandrov’s theorem, weighted Delaunay triangulations, and mixed volumes

Alexander I. Bobenko, Ivan Izmestiev (2008)

Annales de l’institut Fourier

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We present a constructive proof of Alexandrov’s theorem on the existence of a convex polytope with a given metric on the boundary. The polytope is obtained by deforming certain generalized convex polytopes with the given boundary. We study the space of generalized convex polytopes and discover a connection with weighted Delaunay triangulations of polyhedral surfaces. The existence of the deformation follows from the non-degeneracy of the Hessian of the total scalar curvature of generalized...

Klein polyhedra and lattices with positive norm minima

Oleg N. German (2007)

Journal de Théorie des Nombres de Bordeaux

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A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of ℝ n . It generalizes the concept of continued fraction. In this paper facets and edge stars of vertices of a Klein polyhedron are considered as multidimensional analogs of partial quotients and quantitative characteristics of these “partial quotients”, so called determinants, are defined. It is proved that the facets of all the 2 n Klein polyhedra generated by a lattice Λ have uniformly bounded...