Approximation of the Euclidean ball by polytopes
Volume 173 / 2006
Studia Mathematica 173 (2006), 1-18
MSC: Primary 52A20.
DOI: 10.4064/sm173-1-1
Abstract
There is a constant $c$ such that for every $n\in\mathbb N$, there is an $N_{n}$ so that for every $N\geq N_{n}$ there is a polytope $P_{}$ in $\mathbb R^{n}$ with $N$ vertices and $$ \mathop{\rm vol}\nolimits _{n}(B_{2}^{n}\mathbin{\triangle} P) \leq c \mathop{\rm vol}\nolimits _{n}(B_{2}^{n})N^{-\frac{2}{n-1}} $$ where $B_{2}^{n}$ denotes the Euclidean unit ball of dimension $n$.
