## The centro-affine Minkowski problem for polytopes.(English)Zbl 1331.53016

Let $$\mu$$ be a discrete measure on the unit sphere $$S^{n-1}$$. A finite subset $$U$$ of $$S^{n-1}$$ is said to be in general position if any $$k$$ elements of $$U$$, $$1\leq k \leq n$$, are linearly independent. The author proves that $$\mu$$ is the centro-affine surface area measure of a polytope whose outer unit normals are in general position if and only if the support of $$\mu$$ is in general position and not contained in a closed hemisphere.

### MSC:

 53A15 Affine differential geometry 52B11 $$n$$-dimensional polytopes
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