52Bxx Polytopes and polyhedra
This subtopic introduces the core ideas in polytopes and polyhedra, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Specific topics
52B05 Combinatorial properties of polytopes and polyhedra
Overview
Combinatorial properties of polytopes and polyhedra. This topic develops the theory of polytopes and polyhedra, including combinatorial, geometric, and algorithmic viewpoints.
Related Wikipedia Page
Wikipedia: Polytope
Useful Links
Key Ideas
- face lattices and f-vectors
- realization and rigidity questions
- extremal and algorithmic polytope theory
Typical Uses
Used in discrete optimization, geometric modeling, and the study of high-dimensional combinatorial structure.
Applications
- Linear programming geometry
- Combinatorics
- Computer graphics and modeling
References
Recommended Textbooks
52B10 Three-dimensional polytopes
Overview
Three-dimensional polytopes. This topic develops the theory of polytopes and polyhedra, including combinatorial, geometric, and algorithmic viewpoints.
Related Wikipedia Page
Wikipedia: Polytope
Useful Links
Key Ideas
- face lattices and f-vectors
- realization and rigidity questions
- extremal and algorithmic polytope theory
Typical Uses
Used in discrete optimization, geometric modeling, and the study of high-dimensional combinatorial structure.
Applications
- Linear programming geometry
- Combinatorics
- Computer graphics and modeling
References
Recommended Textbooks
52B11 $n$-dimensional polytopes
Overview
$n$-dimensional polytopes. This topic develops the theory of polytopes and polyhedra, including combinatorial, geometric, and algorithmic viewpoints.
Related Wikipedia Page
Wikipedia: Polytope
Useful Links
Key Ideas
- face lattices and f-vectors
- realization and rigidity questions
- extremal and algorithmic polytope theory
Typical Uses
Used in discrete optimization, geometric modeling, and the study of high-dimensional combinatorial structure.
Applications
- Linear programming geometry
- Combinatorics
- Computer graphics and modeling
References
Recommended Textbooks
52B12 Special polytopes (linear programming, centrally symmetric, etc.)
Overview
Special polytopes (linear programming, centrally symmetric, etc.). This topic develops the theory of polytopes and polyhedra, including combinatorial, geometric, and algorithmic viewpoints.
Related Wikipedia Page
Wikipedia: Polytope
Useful Links
Key Ideas
- face lattices and f-vectors
- realization and rigidity questions
- extremal and algorithmic polytope theory
Typical Uses
Used in discrete optimization, geometric modeling, and the study of high-dimensional combinatorial structure.
Applications
- Linear programming geometry
- Combinatorics
- Computer graphics and modeling
References
Recommended Textbooks
52B15 Symmetry properties of polytopes
Overview
Symmetry properties of polytopes. This topic develops the theory of polytopes and polyhedra, including combinatorial, geometric, and algorithmic viewpoints.
Related Wikipedia Page
Wikipedia: Polytope
Useful Links
Key Ideas
- face lattices and f-vectors
- realization and rigidity questions
- extremal and algorithmic polytope theory
Typical Uses
Used in discrete optimization, geometric modeling, and the study of high-dimensional combinatorial structure.
Applications
- Linear programming geometry
- Combinatorics
- Computer graphics and modeling
References
Recommended Textbooks
52B20 Lattice polytopes in convex geometry
Overview
Lattice polytopes in convex geometry. This topic develops the theory of polytopes and polyhedra, including combinatorial, geometric, and algorithmic viewpoints.
Related Wikipedia Page
Wikipedia: Polytope
Useful Links
Key Ideas
- face lattices and f-vectors
- realization and rigidity questions
- extremal and algorithmic polytope theory
Typical Uses
Used in discrete optimization, geometric modeling, and the study of high-dimensional combinatorial structure.
Applications
- Linear programming geometry
- Combinatorics
- Computer graphics and modeling
References
Recommended Textbooks
52B22 Shellability for polytopes and polyhedra
Overview
Shellability for polytopes and polyhedra. This topic develops the theory of polytopes and polyhedra, including combinatorial, geometric, and algorithmic viewpoints.
Related Wikipedia Page
Wikipedia: Polytope
Useful Links
Key Ideas
- face lattices and f-vectors
- realization and rigidity questions
- extremal and algorithmic polytope theory
Typical Uses
Used in discrete optimization, geometric modeling, and the study of high-dimensional combinatorial structure.
Applications
- Linear programming geometry
- Combinatorics
- Computer graphics and modeling
References
Recommended Textbooks
52B35 Gale and other diagrams
Overview
Gale and other diagrams. This topic develops the theory of polytopes and polyhedra, including combinatorial, geometric, and algorithmic viewpoints.
Related Wikipedia Page
Wikipedia: Polytope
Useful Links
Key Ideas
- face lattices and f-vectors
- realization and rigidity questions
- extremal and algorithmic polytope theory
Typical Uses
Used in discrete optimization, geometric modeling, and the study of high-dimensional combinatorial structure.
Applications
- Linear programming geometry
- Combinatorics
- Computer graphics and modeling
References
Recommended Textbooks
52B40 Matroids in convex geometry
Overview
Matroids in convex geometry. This topic develops the theory of polytopes and polyhedra, including combinatorial, geometric, and algorithmic viewpoints.
Related Wikipedia Page
Wikipedia: Polytope
Useful Links
Key Ideas
- face lattices and f-vectors
- realization and rigidity questions
- extremal and algorithmic polytope theory
Typical Uses
Used in discrete optimization, geometric modeling, and the study of high-dimensional combinatorial structure.
Applications
- Linear programming geometry
- Combinatorics
- Computer graphics and modeling
References
Recommended Textbooks
52B45 Dissections and valuations (Hilbert's third problem, etc.)
Overview
Dissections and valuations (Hilbert's third problem, etc.). This topic develops the theory of polytopes and polyhedra, including combinatorial, geometric, and algorithmic viewpoints.
Related Wikipedia Page
Wikipedia: Polytope
Useful Links
Key Ideas
- face lattices and f-vectors
- realization and rigidity questions
- extremal and algorithmic polytope theory
Typical Uses
Used in discrete optimization, geometric modeling, and the study of high-dimensional combinatorial structure.
Applications
- Linear programming geometry
- Combinatorics
- Computer graphics and modeling
References
Recommended Textbooks
52B55 Computational aspects related to convexity
Overview
Computational aspects related to convexity. This topic develops the theory of polytopes and polyhedra, including combinatorial, geometric, and algorithmic viewpoints.
Related Wikipedia Page
Wikipedia: Polytope
Useful Links
Key Ideas
- face lattices and f-vectors
- realization and rigidity questions
- extremal and algorithmic polytope theory
Typical Uses
Used in discrete optimization, geometric modeling, and the study of high-dimensional combinatorial structure.
Applications
- Linear programming geometry
- Combinatorics
- Computer graphics and modeling
References
Recommended Textbooks
52B60 Isoperimetric problems for polytopes
Overview
Isoperimetric problems for polytopes. This topic develops the theory of polytopes and polyhedra, including combinatorial, geometric, and algorithmic viewpoints.
Related Wikipedia Page
Wikipedia: Polytope
Useful Links
Key Ideas
- face lattices and f-vectors
- realization and rigidity questions
- extremal and algorithmic polytope theory
Typical Uses
Used in discrete optimization, geometric modeling, and the study of high-dimensional combinatorial structure.
Applications
- Linear programming geometry
- Combinatorics
- Computer graphics and modeling
References
Recommended Textbooks
52B70 Polyhedral manifolds
Overview
Polyhedral manifolds. This topic develops the theory of polytopes and polyhedra, including combinatorial, geometric, and algorithmic viewpoints.
Related Wikipedia Page
Wikipedia: Polytope
Useful Links
Key Ideas
- face lattices and f-vectors
- realization and rigidity questions
- extremal and algorithmic polytope theory
Typical Uses
Used in discrete optimization, geometric modeling, and the study of high-dimensional combinatorial structure.
Applications
- Linear programming geometry
- Combinatorics
- Computer graphics and modeling
References
Recommended Textbooks