Its very difficult to fill the vector array a way that all the outside-faces of the tetrahedron are rendered.
That means, if your inside the tetrahedron, you should see nothing of the tetrahedron, but from th eoutside, you can't see in the inside of the tetrahedron.
now i hoped, that somebody found an algorithm, that auto sorts the points.
it should look like that:
void sorttetrahedron(Vector in[4],Vector& out[4]);
I'm not sure if this is useful but the usual way (used in openGL etc) to deal with inside/outside of a shape is to have faces which are ordered lists of points around the face.
Normally the face points are ordered anticlockwise as you look at the shape from the outside. Then they come out clockwise if you are looking at the face from the inside of the shape.
...something like the "Painter's algorithm" is coming to mind from way back. Maybe try searching for that and similar algorithms if you want to do the work yourself.