Hello everyone!

I was wondering if anyone out there could help me with some 3d geometry transformations.

What I've got:

I have a tetrahedron (A) in Cartesian space, centred at the origin, with vertices at:

(1,1,1) , (-1,-1,1) , (-1,1-1) & (1,-1,-1).

What I would like:

A tetrahedron (B) with vertices at:

(-1,-1,-1), (0,-1,0), (-1,0,0), (0,0,-1)

The question:

How does one find the transformation matrix to transform tetrahedron A into tetrahedron B?

Any help will be greatly appreciated