Maximal Dimension of Unit Simplices

Abstract. 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.