# Are the 14 Bravais lattices really distinct?

I have learned that there are 14 distinct Bravais lattices in 3D and any other thought lattice form could be reduced to or expressed in one of these 14 forms. But the primitive unit cell for f.c.c lattice is seen to be a special case of trigonal (rhombohedral) lattice (with angles equal to 60 deg). A similar case is true for b.c.c lattice. So, is f.c.c really distinct while it could be expressed as a special case of trigonal lattice? (I also asked this in mathematics stack.)

• In the special case of $\alpha=\beta=\gamma=60^\circ$ it does have the same primitive vectors as FCC lattice, thus it coincides with it. How can their symmetries be different? Jan 20 '15 at 13:26