A characterization of all equilateral triangles in \Bbb Z^3

This paper is a continuation of previous work of the authors. We extend one of the theorems that gave a way to construct equilateral triangles whose vertices have integer coordinates to the general situation. An approximate extrapolation formula for the sequence ET(n) of all equilateral triangles with vertices in $\{0,1,2,\mathrm{.}\mathrm{.}\mathrm{.},n{\}}^3$ (A 102698) is given and the asymptotic behavior of this sequence is analyzed.