for the FCC cubic, there are 12 slip systems: 4 {111} planes and 3 <110> directions... what i don't understand is why are there 4{111} planes instead of 1?
In a cube, you'll find you can draw 8 {1,1,1} planes. However, you'll also see that only 4 of these are unique - the other 4 being parallel to these and separated from them by distance of a/sqrt(3), where 'a' is the cube edge. What I don't understand is why there are only 3 <110> directions when it looks to me like there should be 6 (2 face diagonals on each of the 3 faces).
Rotational symmetry - rotate the cube 90° about the normal to the face plane, and one face diagonal transforms to the other (perpendicular) diagonal. Or rotate the cube 180° about the normal to the base and the <110> becomes <1[itex]\bar1[/itex]0>.
Doesn't this argue that there is only one relevant <110> direction? After all, I can generate the other 5 face diagonals from any one, using a combination of symmetry preserving rotations. Yikes! I've completely lost touch with basic crystallography - time to hit the books.