Miller indices can be tricky (link). But for cubic crystals, they are just the x, y, and z components of a short vector perpendicular to the that facet.
The top of this cubic crystal points the z direction, which is the vector [0, 0, 1] . That makes this the (001) facet. Its front points in the x direction, making it the (100) facet. Note how [ ] brackets denote a vector, and ( ) brackets denote a plane.
But for a crystal with cubic symmetry, the atomic structures of the side, top and bottom facets are identical. Those six planes: (100), (010), (001), (-100), (0-10), (00-1) thus constitute a "family" of equivalent planes, labeled {100} - using yet another type of bracket!
On this cube, the twelve facets of {110} family are also labeled: (110), (011), (101), (-110), (1-10), (0-11), (01-1), (-101), (10-1), (-1-10), (0-1-1), (-10-1). As are the eight facets of the {111} family.
