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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

3 votes

Can I find $n$ points on the boundary of an $n$-dimensional ball with certain properties?

It is not possible for $n>2$. Pick any point $v$ and consider the cone spanned by all tangent rays. Clearly that cone has to be a subset of the solution, as otherwise you would miss part of the ball. …
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