Given a regular Tetrahedron *A* (i.e. each edge of *A* has same length), is it possible to split *A* into several smaller regular tetrahedra of equal size? I.e. smaller tetrahedra should completely fill volume of *A*, and they should not overlap.

This can be done in 2D with a triangle and square, and it can be done in 3D with cube (i.e. you can split cube into several smaller cubes of equal size). But I see no way to do same thing in 3D with tetrahedron.

If this can be done, how (how smaller tetrahedra should be positioned)?

If this cannot be done, is there a proof that this is impossible?

P.S. I'm not a mathematician, and this is not a homework, but I'd like to know how/if this can be done.