Maximal dimension of unit simplices

Christian Elsholtz*, Walter Klotz

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    For an arbitrary field F the maximal number ω(Fn) of points in Fn 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(Fn) 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(Qn) = n and for almost all odd n that ω(Qn) = n - 1.

    Original languageEnglish
    Pages (from-to)167-177
    Number of pages11
    JournalDiscrete & Computational Geometry
    Issue number1
    Publication statusPublished - 2005

    ASJC Scopus subject areas

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


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