  Metal crystals with tetrahedral packing are known as Frank-Kasper phases with
large unit cells with the number of atoms from hundreds to thousands. The main
factors of the formation and stability of these phases are the atomic size
ratio and the number of valence electrons per atom. The significance of the
electronic energy contribution is analyzed within the Fermi sphere - Brillouin
zone interactions model for several typical examples: Cu4Cd3, Mg2Al3 with over
thousand atoms per cell, and for icosahedral quasicrystal approximants with 146
to 168 atoms per cell. Our analysis shows that to minimize the crystal energy,
it is important that the Fermi sphere (FS) is in contact with the Brillouin
zones that are related to the strong diffraction peaks: the zones either
inscribe the FS or are circumscribed by the FS creating contact at edges or
vertices.
