In an fcc unit cell, atoms are numbered as shown below. The atoms not touching each other are (Atom numbered 3 is face centre of front face)

In fcc structure, corner atoms do not touch each other (atoms I and 2),but every face centre atom touches corners. Moreover, every face centre atom touches every other face centre atom provided it is not the opposite face centre atom in an fcc unit cell. i.  Atoms 3 and 4 are touching each other where centre-to-centre distance = a2ii. Atoms 1 and 2 are not touching each otheriii. Atoms 2 and 4 are touching each other where centre-to-centre distance =a2