Results 1 to 10 of about 181 (122)
A note on non-commutative polytopes and polyhedra [PDF]
Advances in Geometry, 2021 Abstract It is well-known that every polyhedral cone is finitely generated (i.e. polytopal), and vice versa. Surprisingly, the two notions differ almost always for non-commutative versions of such cones, as was recently proved by different authors. In this note we give a direct and constructive proof of the statement.
Beatrix Huber, Tim Netzer
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Polytopes, polyhedra, and the Farkas lemma [PDF]
, 2022 The Farkas lemma is proved and applied to obtain a structure theorem for polyhedra. These notes are based on a talk in the New York Number Theory Seminar on October, 20, 2022.
Melvyn B. Nathanson
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Beta polytopes and Poisson polyhedra: f-vectors and angles [PDF]
Advances in Mathematics, 2020 We study random polytopes of the form $[X_1,\ldots,X_n]$ defined as convex hulls of independent and identically distributed random points $X_1,\ldots,X_n$ in $\mathbb{R}^d$ with one of the following densities: $$ f_{d, } (x) = c_{d, } (1-\|x\|^2)^ , \qquad \|x\| < 1, \quad \text{(beta distribution, $ >-1$)} $$ or $$ \tilde f_{d, } (x ...
Zakhar Kabluchko +2 more
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Classifying Regular Polyhedra and Polytopes using Wythoff's Construction [PDF]
, 2020 Wythoff's construction associates a uniform polytope to a Coxeter diagram whose vertices are decorated with crosses, which indicate the subgroup stabilizing a generic point. Champagne, Kjiri, Patera, and Sharp remarked that by associating more information to a Coxeter diagram, one can furthermore determine the types and number of faces of such a ...
Spencer Whitehead
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Concentration and moderate deviations for Poisson polytopes and polyhedra [PDF]
Bernoulli, 2018 The convex hull generated by the restriction to the unit ball of a stationary Poisson point process in the $d$-dimensional Euclidean space is considered. By establishing sharp bounds on cumulants, exponential estimates for large deviation probabilities are derived and the relative error in the central limit theorem on a logarithmic scale is ...
Julian Grote, Christoph Thaele
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Tail diameter upper bounds for polytopes and polyhedra [PDF]
, 2016 15 ...
J. Mackenzie Gallagher, Edward D. Kim
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Notes on Convex Sets, Polytopes, Polyhedra, Combinatorial Topology, Voronoi Diagrams and Delaunay Triangulations [PDF]
, 2008 Some basic mathematical tools such as convex sets, polytopes and combinatorial topology, are used quite heavily in applied fields such as geometric modeling, meshing, computer vision, medical imaging and robotics. This report may be viewed as a tutorial and a set of notes on convex sets, polytopes, polyhedra, combinatorial topology, Voronoi Diagrams ...
Jean Gallier
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Investigating polyhedra by oracles and analyzing simple extensions of polytopes
, 2016 von Dipl.-Comp.-Math.
Matthias Walter
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InformationInspired by Critchlow [1], and Grünbaum and Shephard [2], previous work has proposed an integral 2.5D cubic schema of the regular and semi-regular polyhedra and polygonal tessellations of the plane for each class of symmetry. This schema is differentiated into an upper and lower layer of 4 polytopes each, and characterized by corresponding pairs of ...
Robert C. Meurant
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InformationIn this paper, I apply my 2.5D cubic schema of polyhedra by the separation of faces (SoF), and rhombic schema of faces (RSoF), to generate core–shell and core–multi-shell geometries for Class II of {2,3,4} symmetry, with respect to the interlayer cells they generate. This morphology of polyhedra by symmetry class with the inclusion of a null element VP
Robert C. Meurant
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