### Abstract

For an arbitrary field F the maximal number ω(F^{n}) of points in F^{n} mutually distance 1 apart with respect to the standard inner product is investigated. If the characteristic char(F) is different from 2, then the values of ω(F^{n}) lie between n - 1 and n + 2. In particular, we answer completely for which n a simplex of q points with edge length 1 can be embedded in rational n-space. Our results imply for almost all even n that ω(Q^{n}) = n and for almost all odd n that ω(Q^{n}) = n - 1.

Original language | English |
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Pages (from-to) | 167-177 |

Number of pages | 11 |

Journal | Discrete & computational geometry |

Volume | 34 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2005 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology

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## Cite this

Elsholtz, C., & Klotz, W. (2005). Maximal dimension of unit simplices.

*Discrete & computational geometry*,*34*(1), 167-177. https://doi.org/10.1007/s00454-004-1155-x