Polyhedral combinatorics

Gale diagram

In the mathematical discipline of polyhedral combinatorics, the Gale transform turns the vertices of any convex polytope into a set of vectors or points in a space of a different dimension, the Gale diagram of the polytope. It can be used to describe high-dimensional polytopes with few vertices, by transforming them into sets of points in a space of a much lower dimension. The process can also be reversed, to construct polytopes with desired properties from their Gale diagrams. The Gale transform and Gale diagram are named after David Gale, who introduced these methods in a 1956 paper on neighborly polytopes. (Wikipedia).

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Related pages

Unit vector | Convex hull | Kernel (linear algebra) | Universal vertex | Neighborly polytope | Relative interior | Origin (mathematics) | Vertex figure | Triangular prism | Perles configuration | Enumerative combinatorics | Polyhedral combinatorics | Quadrilateral | Simplex | Square pyramid | Triangular bipyramid | Convex polytope | David Gale | Unit circle | Oriented matroid | Dual matroid | Matrix (mathematics)