A note on the size of the largest ball inside a convex polytope

Let m > 1 be an integer, Bm the set of all unit vectors of R pointing in the direction of a nonzero integer vector of the cube [−1, 1]. Denote by sm the radius of the largest ball contained in the convex hull of Bm. We determine the exact value of sm and obtain the asymptotic equality sm ∼ 2 √ log m . Primary subject classification: 52B11 Secondary subject classification: 52B12 §