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About 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 with the same number of points, but 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.
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