Question: How can I select four points on a sphere to make a regular tetrahedron so that its coordinates are integer numbers?

I have the sphere x^2 + y^2 + z^2 =( 33*sqrt(3))^2 and I want to select four points on a sphere to make a regular tetrahedron so that its coordinates are integer numbers. I see this question is here https://mathematica.stackexchange.com/questions/289123/how-can-i-select-four-points-on-a-sphere-to-make-a-regular-tetrahedron-so-that-i
Time to get result is a problem. 

Please Wait...