We start with a cube, make the middle points at each face. Then choose three middle points, and a corner of the cube, and make the middle point to form a tetrahedral structure. You repeat this at 3 more corners of the cube, as shown in the picture. The white bonds are made simply to mantain joined the structure when copied.
We then make copies to join them, and then can delete the white bonds.
This is how it looks like, after gluing copies of the fundamental cell.
Some more copies of copies together. 

You can continue as far as you like. The diamond cubic crystal structure looks impressive. It is much better than in this picture with the glasses of virtual reality.