New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square   theorem
  In this paper we provide a new parametrization for the diophantine equation $A^2+B^2+C^2=3D^2$ and give a series of corollaries. We discuss some connections with Lagrange's four-square theorem. As applications, we find new parameterizations of equilateral triangles and regular tetrahedrons having integer coordinates in three dimensions. 
Eugen J. Ionascu
math.NT