A characterization of regular tetrahedra in Z3

In this note we characterize all regular tetrahedra whose vertices in R 3 have integer coordinates. The main result is a consequence of the characterization of all equilateral triangles having integer coordinates ([3]). Previous work on this topic began in [4]. We will use this characterization to point out some corollaries. The number of such tetrahedra whose vertices are in the finite set {0, 1, 2, ..., n} 3 , n ∈ N, is related to the sequence A103158 in the Online Encyclopedia of Integer Sequences ([9])