A Brillouin zone is defined as a Wigner~Secitz primitive cell in the reciprocal lattice [1,2].
The construction of the first Brillouin zone for two different 2D lattices are shown below:
The construction procedure for 3D lattices is basically the same as for 2D lattices. In the image below, the first Brillouin zone of FCC lattice, a truncated octahedron, showing symmetry labels for high symmetry lines and points are shown:
My question is: how the labels of the high symmetry points are defined and associated with the vertices, edges, faces and lines of the surface?
 Ashcroft, Neil W. & Mermin, N. David, Solid State Physics
 Kittel, Charles, Introduction to Solid State Physics