I'm trying to render some $3D$ graphics with a bunch of tetrahedra. I'm trying to figure out how to rotate one tetrahedron such that it will be perfectly face-to-face with another tetrahedron. If this is confusing, multiple tetrahedra touching face to face would look like this.
I'm using OpenGL to programmatically rotate objects, so I can only rotate on one of the three axes at a time. For example, I can rotate clockwise $20^\circ$ in $X$, then counterclockwise $45^\circ$ in $Z$, etc.
Thanks for any help, let me know if you need more clarification.