  Using a tight-binding approach we study theoretically the nature of surface
states in Pb0.4Sn0.6Te - the newly discovered
topological-crystalline-insulator. Apart from the studied before (001) surface
states, two other surface families, {011} and {111}, in which the mirror
symmetry of the crystal's rock-salt structure plays the same role in
topological protection, are considered. Our calculations show that while in
(111) surface states of (Pb,Sn)Te four single topologically protected
Dirac-cones should appear, for the (110) surface states the protection is
lifted for two L points. In this case, instead of the Dirac points energy gaps
occur in the surface states, due to the interaction between the two L valleys.
In all studied cases a chiral spin texture is obtained.
