A Note on the Size of the Largest Ball Inside a Convex Polytope

Details A Note on the Size of the Largest Ball Inside a Convex Polytope A Note on the Size of the Largest Ball Inside a Convex Polytope

2005-05-14

arxiv.org/abs/math/0505301v2

Period. Math. Hungar. Vol. 51, No. 2 (2005), pp. 15-18

Mathematics

Metric Geometry

Scientific paper

10.1007/s10998-005-0026-4

Let $m>1$ be an integer, $B_m$ the set of all unit vectors of $\Bbb R^m$
pointing in the direction of a nonzero integer vector of the cube $[-1, 1]^m$.
Denote by $s_m$ the radius of the largest ball contained in the convex hull of
$B_m$. We determine the exact value of $s_m$ and obtain the asymptotic equality
$s_m\sim\frac{2}{\sqrt{\log m}}$.

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