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On convex decision regions in deep network representations. [PDF]
Nat CommunTětková L +7 more
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Parallel Mechanisms for Multiscale Motion Using Twisted Wire Actuation: Designing for Microworkspace and Dexterity. [PDF]
J Mech RobotAhronovich EZ, Turner JH, Simaan N.
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The DIRAC framework: Geometric structure underlies roles of diversity and accuracy in combining classifiers. [PDF]
Patterns (N Y)Sniatynski MJ +4 more
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Fragmenting any Parallelepiped into a Signed Tiling. [PDF]
Discrete Comput GeomDoolittle J, McDonough A.
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Benders Decomposition Using Graph Modeling and Multi-Parametric Programming. [PDF]
Ind Eng Chem ResBrahmbhatt P +3 more
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Izvestiya: Mathematics, 2017
Summary: We describe the combinatorics of three families of simple 3-dimensional polytopes which play an important role in various problems of algebraic topology, hyperbolic geometry, graph theory, and their applications. The first family \(\mathcal{P}_{\leqslant 6}\) consists of simple polytopes with at most hexagonal faces.
Buchstaber, Victor M. +1 more
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Summary: We describe the combinatorics of three families of simple 3-dimensional polytopes which play an important role in various problems of algebraic topology, hyperbolic geometry, graph theory, and their applications. The first family \(\mathcal{P}_{\leqslant 6}\) consists of simple polytopes with at most hexagonal faces.
Buchstaber, Victor M. +1 more
openaire +2 more sources
Regularly Faceted Three-Dimensional Polytopes
2022It is shown that known classification of convex polyhedrons with sides from correct polygons offered by V.A. Zallgaller as full transfer of all possible convex figures of this type is far from completeness. There exist nine new convex polyhedrons with sides from correct polygons and the impossibility of existence of two figures from Zallgeller ...
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Regular and Semi-Regular Three-Dimensional Polytopes
2022The convex three-dimensional regular and semiregular polyhedrons were investigated using mental mechanical operations on polyhedrons. They include cutting polyhedrons (cutting off vertices), the necessary deformations of the section sections to shape the sections into regular polygons, and rotating parts of the polyhedrons relative to each other. There
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Typical faces of extremal polytopes with respect to a thin three-dimensional shell
Periodica Mathematica Hungarica, 2006Given ]]> ]]> ]]> ]]> ]]> r>1$, we search for the convex body of minimal volume in $\mathbb{E}^3$ that contains a unit ball, and whose extreme points are of distance at least $r$ from the centre of the unit ball. It is known that the extremal body is the regular octahedron and icosahedron for suitable values of $r$. In this paper we
Károly Böröczky +2 more
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