Maximal Dimension of Unit Simplices

For an arbitrary field F the maximal number omega(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 omega(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 omage(Q n ) = n and for almost all odd n that omega(Q n ) = n - 1. [PUBLICATION ABSTRACT]