The Infimum of the Volumes of Convex Polytopes
نویسنده
چکیده
We prove the theorem mentioned in the title, for Rn, where n ≥ 3. The case of the simplex was known previously. Also, the case n = 2 was settled, but there the infimum was some well-defined function of the side lengths. We also consider the cases of spherical and hyperbolic n-spaces. There we give some necessary conditions for the existence of a convex polytope with given facet areas, and some partial results about sufficient conditions for the existence of (convex) tetrahedra. 2010 Mathematical Subject Classification: 52B11 (primary), 52A38, 52A55 (secondary).
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تاریخ انتشار 2013