# Why is the silicon crystalline structure is called cubic?

Silicon has a valence 4 (electron shells: 2, 8, 4), hence having 4 neighbors in the 3D space, which for me should appear as a mesh of regular tetrahedrons, with the Si atoms at the centre.

But silicon's crystal structure is Face Centered Diamond Cubic.

From a tetrahedral mesh, I can obtain a hexahedral mesh by proper selection of vertex... But why isn't the mesh defined as tetrahedrons, which could be more intuitive? Or it is indeed a hexahedral mesh?

Each tetrahedron contains two Si atoms, one in the center and a quarter on each corner of the tetrahedron. However, different unit cells can be used to describe the same crystal lattice. It is easier to visualize the diamond lattice by the depicted conventional (not primitive) cubic unit cell with side length $a$. It can be seen that this corresponds to two interpenetrating face centered cubic Bravais point lattices that are displaced with respect to each other by a quarter of the cube's diagonal.