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How does one translate from convex hull to a set of facets (inequalities)? [duplicate]

Suppose I have defined a convex set as the convex hull of a set of points. (I know that all these points are "extremal points" of the convex set.) I know want to translate this description of the ...
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Intersecting a convex polytope with the unit sphere

I have a list of $m$ affine inequalities in $n$ variables of the following form $$a_1 x_1 + \cdots + a_n x_n \leq c_n$$ I would like to know whether there is any point on the unit sphere in $\...
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