### Abstract

There is a constant c such that for every n ∈ ℕ, there is an N _{n} so that for every N ≥ N _{n} there is a polytope P in ℝ ^{n} with N vertices and vol _{n}(B _{2} ^{n} Δ P) ≤ c vol _{n}(B _{2} ^{n}) N ^{-2/n-1} where B _{2} ^{n} denotes the Euclidean unit ball of dimension n.

Original language | English (US) |
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Pages (from-to) | 1-18 |

Number of pages | 18 |

Journal | Studia Mathematica |

Volume | 173 |

Issue number | 1 |

DOIs | |

State | Published - Jun 16 2006 |

### Keywords

- Approximation by polytopes
- Convex body

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## Cite this

Ludwig, M., Schütt, G., & Werner, E. (2006). Approximation of the Euclidean ball by polytopes.

*Studia Mathematica*,*173*(1), 1-18. https://doi.org/10.4064/sm173-1-1