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APPLICATIONS OF GEOMETRY
CONVEX SETS AND THE COMBINATORIAL
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affine space angle assume axioms barycentric coordinates bounded circles closed convex set closure compact cone conic consider conv convex hull convex set coordinates corresponding Coxeter curve d-polytope defined definition denote derivative determined dilatation dimensional director space discussion edges equiaffinity Euclidean geometry Euclidean space example exists extreme points facets finite formula function theorem given Gleason graph Grunbaum H. S. M. Coxeter halfspaces Helly's theorem higher dimensions hyperbolic space implies inequality integral integral geometry interior intersection invariant point inversive plane isometry isomorphism Jordan content k-dimensional Klee lecture linear algebra linear transformations mapping mathematics matrix metric Minkowski number of vertices obtain orthogonal parallel pencil perpendicular polygon poonem Prenowitz problem proof properties prove real numbers reflections rel int result rotation scalar segment similar solution sphere Steenrod subset tangent tion topological translation triangle variables vector space vertex volume