2007, ISBN 9780521857574, Volume 9780521857574, xiii, 472

Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a...

Data processing | Models | Polyhedra

Data processing | Models | Polyhedra

Book

2005, Springer monographs in mathematics, ISBN 9783540231585, xi, 539

Convex Polyhedra is one of the classics in geometry. There simply is no other book with so many of the aspects of the theory of 3-dimensional convex polyhedra...

Polyhedra | Discrete groups | Convex surfaces

Polyhedra | Discrete groups | Convex surfaces

Book

Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, 07/2018, Volume 115, Issue 29, pp. E6690 - E6696

Low-dimensional objects such as molecular strands, ladders, and sheets have intrinsic features that affect their propensity to fold into 3D objects....

Origami | Cooperativity | Polyhedra nets | Folding | LINKING RIGID BODIES | cooperativity | MULTIDISCIPLINARY SCIENCES | folding | origami | KIRIGAMI | CONVEX POLYTOPES | MECHANISMS | polyhedra nets | MOLECULAR-DYNAMICS SIMULATIONS | Mathematical research | Polyhedra | Research | INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY | Other Topics | Science & Technology | Physical Sciences | PNAS Plus

Origami | Cooperativity | Polyhedra nets | Folding | LINKING RIGID BODIES | cooperativity | MULTIDISCIPLINARY SCIENCES | folding | origami | KIRIGAMI | CONVEX POLYTOPES | MECHANISMS | polyhedra nets | MOLECULAR-DYNAMICS SIMULATIONS | Mathematical research | Polyhedra | Research | INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY | Other Topics | Science & Technology | Physical Sciences | PNAS Plus

Journal Article

Langmuir, ISSN 0743-7463, 10/2017, Volume 33, Issue 42, pp. 11788 - 11796

Hard polyhedra are a natural extension of the hard sphere model for simple fluids, but there is no general scheme for predicting the effect of shape on...

CONVEX-BODIES | PARTICLES | SPHERES | BEHAVIOR | MATERIALS SCIENCE, MULTIDISCIPLINARY | OF-STATE | CHEMISTRY, PHYSICAL | TETRAHEDRA | BODY-FLUIDS | CHEMISTRY, MULTIDISCIPLINARY | EXPANSION | COMPLEX STRUCTURES | CRYSTALLINE

CONVEX-BODIES | PARTICLES | SPHERES | BEHAVIOR | MATERIALS SCIENCE, MULTIDISCIPLINARY | OF-STATE | CHEMISTRY, PHYSICAL | TETRAHEDRA | BODY-FLUIDS | CHEMISTRY, MULTIDISCIPLINARY | EXPANSION | COMPLEX STRUCTURES | CRYSTALLINE

Journal Article

Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, 12/2011, Volume 108, Issue 50, pp. 19885 - 19890

Self-assembly has emerged as a paradigm for highly parallel fabrication of complex three-dimensional structures. However, there are few principles that guide a...

Topological compactness | Self assembly | Solders | Geodesy | Polyhedrons | Cubes | Capsid | Octahedrons | Vertices | Icosahedrons | Origami | Viral capsid | Microfabrication | Programmable matter | viral capsid | NETS | DNA | MULTIDISCIPLINARY SCIENCES | origami | SCALES | microfabrication | programmable matter | CONVEX POLYTOPES | CUBE | PRINCIPLES | Models, Molecular | Microscopy, Electron, Scanning | Algorithms | Molecular Conformation | Geometric figures | Usage | Molecular structure | Analysis | Physical Sciences

Topological compactness | Self assembly | Solders | Geodesy | Polyhedrons | Cubes | Capsid | Octahedrons | Vertices | Icosahedrons | Origami | Viral capsid | Microfabrication | Programmable matter | viral capsid | NETS | DNA | MULTIDISCIPLINARY SCIENCES | origami | SCALES | microfabrication | programmable matter | CONVEX POLYTOPES | CUBE | PRINCIPLES | Models, Molecular | Microscopy, Electron, Scanning | Algorithms | Molecular Conformation | Geometric figures | Usage | Molecular structure | Analysis | Physical Sciences

Journal Article

Formal Methods in System Design, ISSN 0925-9856, 8/2019, Volume 54, Issue 1, pp. 27 - 63

In this paper, we study the template polyhedral abstract domain using connections to bilinear optimization techniques. The connections between abstract...

Engineering | Convex optimization | Computer-Aided Engineering (CAD, CAE) and Design | Static analysis | Software Engineering/Programming and Operating Systems | Abstract interpretation | Interior point methods | Circuits and Systems | Bilinear programs | Policy iteration | Electrical Engineering | BRANCH | ITERATION | INVARIANTS | ALGORITHM | RELAXATIONS | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | COMPUTATION | POINT | Mathematical optimization | Analysis | Algorithms

Engineering | Convex optimization | Computer-Aided Engineering (CAD, CAE) and Design | Static analysis | Software Engineering/Programming and Operating Systems | Abstract interpretation | Interior point methods | Circuits and Systems | Bilinear programs | Policy iteration | Electrical Engineering | BRANCH | ITERATION | INVARIANTS | ALGORITHM | RELAXATIONS | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | COMPUTATION | POINT | Mathematical optimization | Analysis | Algorithms

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 10/2016, Volume 56, Issue 3, pp. 592 - 630

We characterize the convex polyhedra P in $${\mathbb {R}}^n$$ R n for which any family of n-dimensional axis-parallel hypercubes centered in P and intersected...

Convex polyhedra | Computational Mathematics and Numerical Analysis | 52B99 | Helly property | 51F99 | 46B20 | Linear programming | Mathematics | Binary intersection property | Absolute 1-Lipschitz retracts | Hyperconvexity | Combinatorics | Injectivity | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | Linear systems | Polyhedra | Equivalence | Metric space | Mathematical analysis | Inequalities | Polyhedrons | Texts

Convex polyhedra | Computational Mathematics and Numerical Analysis | 52B99 | Helly property | 51F99 | 46B20 | Linear programming | Mathematics | Binary intersection property | Absolute 1-Lipschitz retracts | Hyperconvexity | Combinatorics | Injectivity | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | Linear systems | Polyhedra | Equivalence | Metric space | Mathematical analysis | Inequalities | Polyhedrons | Texts

Journal Article

2008, Zurich lectures in advanced mathematics, ISBN 9783037190524, viii, 189

Book

European Journal of Operational Research, ISSN 0377-2217, 07/2018, Volume 268, Issue 1, pp. 37 - 53

•Tools to describe non-overlapping and distance constraints for concave polyhedra.•NLP-model of the packing problem of concave polyhedra with continuous...

Nonlinear optimisation | Concave polyhedra | Mathematical modelling | Continuous rotations | Packing | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | CONVEX POLYTOPES

Nonlinear optimisation | Concave polyhedra | Mathematical modelling | Continuous rotations | Packing | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | CONVEX POLYTOPES

Journal Article

Acta Crystallographica Section A, ISSN 2053-2733, 09/2017, Volume 73, Issue 5, pp. 423 - 425

The formulas for the minimum (minn) and maximum (maxn) names in the classes of convex n‐acra (i.e. n‐vertex polyhedra) are found for any n. The asymptotic...

minimum and maximum names | asymptotic relationships | convex polyhedra and polyacra | CRYSTALLOGRAPHY | CHEMISTRY, MULTIDISCIPLINARY | Polyhedrons | Polyhedra | Convexity | Scattering

minimum and maximum names | asymptotic relationships | convex polyhedra and polyacra | CRYSTALLOGRAPHY | CHEMISTRY, MULTIDISCIPLINARY | Polyhedrons | Polyhedra | Convexity | Scattering

Journal Article

INDIANA UNIVERSITY MATHEMATICS JOURNAL, ISSN 0022-2518, 2018, Volume 67, Issue 3, pp. 1299 - 1326

In this paper, we prove the following rigidity theorem: a generic analytic polyhedron with non-compact automorphism group is biholomorphic to the product of a...

MATHEMATICS | C-2 | BOUNDARY | CONVEX DOMAINS

MATHEMATICS | C-2 | BOUNDARY | CONVEX DOMAINS

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 9/2007, Volume 38, Issue 2, pp. 201 - 230

We study two notions. One is that of spindle convexity. A set of circumradius not greater than one is spindle convex if, for any pair of its points, it...

Computational Mathematics and Numerical Analysis | Convex Hull | Unit Ball | Constant Width | Convex Body | Mathematics | Combinatorics | Face Lattice | MATHEMATICS | KNESER-POULSEN CONJECTURE | SPACES | THEOREMS | PLANE | SETS | POLYTOPES | COMPUTER SCIENCE, THEORY & METHODS | Geometry | Polyhedra

Computational Mathematics and Numerical Analysis | Convex Hull | Unit Ball | Constant Width | Convex Body | Mathematics | Combinatorics | Face Lattice | MATHEMATICS | KNESER-POULSEN CONJECTURE | SPACES | THEOREMS | PLANE | SETS | POLYTOPES | COMPUTER SCIENCE, THEORY & METHODS | Geometry | Polyhedra

Journal Article

Mathematical Programming, ISSN 0025-5610, 6/2014, Volume 145, Issue 1, pp. 19 - 58

Recently, cutting planes derived from maximal lattice-free convex sets have been studied intensively by the integer programming community. An important...

Integer programming | 90C10 | Mathematical Methods in Physics | Polyhedral closures | Cutting planes | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C11 | Mathematics | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITIES | FREE CONVEX-SETS | Studies | Polyhedra | Mathematical analysis | Theorems | Heating | Triangles | Polyhedrons | Mathematical models | Polynomials | Closures

Integer programming | 90C10 | Mathematical Methods in Physics | Polyhedral closures | Cutting planes | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C11 | Mathematics | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITIES | FREE CONVEX-SETS | Studies | Polyhedra | Mathematical analysis | Theorems | Heating | Triangles | Polyhedrons | Mathematical models | Polynomials | Closures

Journal Article

Algorithmica, ISSN 0178-4617, 10/2009, Volume 55, Issue 2, pp. 329 - 345

We present the first exact and robust implementation of the 3D Minkowski sum of two non-convex polyhedra. Our implementation decomposes the two polyhedra into...

Data Structures, Cryptology and Information Theory | Computer Systems Organization and Communication Networks | Algorithms | Exact arithmetic | Minkowski sum | Mathematics of Computing | Decomposition of polyhedra into convex pieces | Computer Science | Theory of Computation | Tight passage | Algorithm Analysis and Problem Complexity | Nef polyhedra | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | CONSTRUCTION | TRIANGLES | ALGORITHMS | Robots

Data Structures, Cryptology and Information Theory | Computer Systems Organization and Communication Networks | Algorithms | Exact arithmetic | Minkowski sum | Mathematics of Computing | Decomposition of polyhedra into convex pieces | Computer Science | Theory of Computation | Tight passage | Algorithm Analysis and Problem Complexity | Nef polyhedra | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | CONSTRUCTION | TRIANGLES | ALGORITHMS | Robots

Journal Article

Mathematics of Operations Research, ISSN 0364-765X, 5/2018, Volume 43, Issue 2, pp. 580 - 597

We introduce an iterative method for solving linearly constrained optimization problems, whose nonsmooth nonconvex objective function is defined as the...

minmax problems | nonconvex optimization | piecewise-concave | nonsmooth optimization | Nonsmooth optimization | Nonconvex optimization | Minmax problems | Piecewise-concave | PROXIMAL BUNDLE METHOD | NONDIFFERENTIABLE OPTIMIZATION | MATHEMATICS, APPLIED | CONVEX MAXIMIZATION PROBLEMS | ALGORITHM | NONSMOOTH FUNCTIONS | ROBUST OPTIMIZATION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | VARIABLE NEIGHBORHOOD SEARCH | SUBGRADIENT METHODS | ORACLES | Analysis | Algorithms | Polyhedra | Functional equations | Mathematical research | Functions | Research | Mathematical optimization

minmax problems | nonconvex optimization | piecewise-concave | nonsmooth optimization | Nonsmooth optimization | Nonconvex optimization | Minmax problems | Piecewise-concave | PROXIMAL BUNDLE METHOD | NONDIFFERENTIABLE OPTIMIZATION | MATHEMATICS, APPLIED | CONVEX MAXIMIZATION PROBLEMS | ALGORITHM | NONSMOOTH FUNCTIONS | ROBUST OPTIMIZATION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | VARIABLE NEIGHBORHOOD SEARCH | SUBGRADIENT METHODS | ORACLES | Analysis | Algorithms | Polyhedra | Functional equations | Mathematical research | Functions | Research | Mathematical optimization

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 12/2019, Volume 203, Issue 1, pp. 337 - 346

We verify the infinitesimal inversive rigidity of almost all triangulated circle polyhedra in the Euclidean plane $${\mathbb {E}}^{2}$$ E 2 , as well as the...

Inversive rigidity | Circle packing | Convex and Discrete Geometry | Algebraic Geometry | Mathematics | Hyperbolic Geometry | Projective Geometry | Topology | Differential Geometry | Circle polyhedron

Inversive rigidity | Circle packing | Convex and Discrete Geometry | Algebraic Geometry | Mathematics | Hyperbolic Geometry | Projective Geometry | Topology | Differential Geometry | Circle polyhedron

Journal Article

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, ISSN 0138-4821, 3/2016, Volume 57, Issue 1, pp. 51 - 66

Triangulations of 3-dimensional polyhedron are partitions of the polyhedron with tetrahedra in a face-to-face fashion without introducing new vertices....

Geometry | Polyhedron | Triangulation | Algebra | 52C22 | Convex and Discrete Geometry | Algebraic Geometry | Mathematics | Tiling | 52A15

Geometry | Polyhedron | Triangulation | Algebra | 52C22 | Convex and Discrete Geometry | Algebraic Geometry | Mathematics | Tiling | 52A15

Journal Article

2005, Contemporary mathematics, ISBN 9780821834596, Volume 374, xi, 191

Book

Acta Crystallographica Section A, ISSN 2053-2733, 05/2017, Volume 73, Issue 3, pp. 271 - 273

The paper reports the combinatorial types of convex n‐acra (i.e. n‐vertex polyhedra) for which the minimum (min.) and maximum (max.) names are attained. Hence,...

adjacency matrix | maximum name | edge graph | convex polyhedra | minimum name | CRYSTALLOGRAPHY | CHEMISTRY, MULTIDISCIPLINARY | Names | Foundations | Polyhedra | Algorithms | Mathematical analysis | Polyhedrons | Graphs | Combinatorial analysis

adjacency matrix | maximum name | edge graph | convex polyhedra | minimum name | CRYSTALLOGRAPHY | CHEMISTRY, MULTIDISCIPLINARY | Names | Foundations | Polyhedra | Algorithms | Mathematical analysis | Polyhedrons | Graphs | Combinatorial analysis

Journal Article

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