I would like to know how can I obtain the
coordinates of the vertices of a tetrahedron if I only have its center coordinates and the distance from the center to a vertex (the alignment could be with a face aligned with the X plane).
Thank you, thank you!
Not enough info. Are we to assume the tetrahedron is regular?
The points (1,1,1), (-1,1,-1), (1,-1,-1), and (-1,-1,1) define a regular tetrahedron with a center at (0,0,0) and a distance from the center to the vertex of root(1.5).
To get one of the faces aligned with the x-z plane, you need to rotate the vertices. You should be able to figure out how much and around which axis.