This animated illustration is from Wikipedia. It demonstrates how spheres generate lines (lattice), triangles, and then a tetrahedron. With that second layer of green spheres emerges the tetrahedral-octahedral couplet. The discipline, known as cubic close packing (ccp), deserves our attention. “The Kepler conjecture states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular.
This conjecture was proven by Thomas C. Hales.” (Wikipedia)