Why Is There No Face Centered Tetragonal?

Symmetry for tetragonal is single four fold axis, which means we can get the same lattice if we rotate the unit cell by 90 degree along C-axis. In case of face centred tetragonal, symmetry number is greater and this symmetry is not considered for tetragonal crystal system.

What is face Centred tetragonal?

One might suppose stretching face-centered cubic would result in face-centered tetragonal, but the face-centered tetragonal is equivalent to the body-centered tetragonal, BCT (with a smaller lattice spacing). BCT is considered more fundamental, and therefore this is the standard terminology. Bravais lattice. Primitive.

Why end centered cubic unit cell is not possible?

In order to have end centered closed packing structure unit cell must possess vectors a≠b≠c, which is absent in case of cubic unit cell due to this cubic unit cell cannot possess end-centred closed packing. The highest symmetry possible for an end centered unit cell is tetragonal.