Convexity/Convex polytopes
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Definition: A convex polytope is the convex hull of a finite number of points. Usually, there will be at least three noncollinear points.
Theorem: A set is a convex polytope if and only if:

 It is not the empty set
 It is bounded
 It is the intersection of a finite number of closed halfspaces.
A simplex in an ndimensional vector space is the convex hull of n+1 points that do not all lie on the same hyperplane. If n=2, a simplex is a triangle; if n=3, it is a tetrahedron.
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