  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
contained in previous work. Then we 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 in N, is related to the sequence A103158 in the Online
Encyclopedia of Integer Sequences.
