Publication

On canonical representations of convex polyhedra

Komei Fukuda
2002
Conference Papers

Abstract

Every convex polyhedron in the Euclidean space $R^d$ admits both H-representation and V-representation. When working with convex polyhedra, in particular large-scale ones in high dimensions, it is useful to have a canonical representation that is minimal and unique up to some elementary operations. Such a representation allows one to compare two H-polyhedra or two V-polyhedra efficiently. In this paper, we define such representations that are simple and can be computed in polynomial time. The key ingredients are redundancy removal for linear inequality systems and affine transformations of polyhedra.

Official source

https://infoscience.epfl.ch/entities/publication/9ce693a3-1a71-41bc-b7cc-13ba70c26ac1

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Komei Fukuda
2002
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/9ce693a3-1a71-41bc-b7cc-13ba70c26ac1

About this result

Related concepts (32)

Polyhedron

In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set. Every convex polyhedron can be constructed as the convex hull of its vertices, and for every finite set of points, not all on the same plane, the convex hull is a convex polyhedron. Cubes and pyramids are examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions.

List of uniform polyhedra

In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry. Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular star polygon faces or vertex figures or both.

Representation theory

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).

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On canonical representations of convex polyhedra

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