From Online Dictionary of Crystallography
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Indices de direction (Fr); Indices de dirección (Sp); Indici di direzione (It); 方向指数 (Ja).
Any direction in a Bravais lattice is identified by a set of N indices (where N is the dimensionality of the space), written in square brackets, called the direction indices.
In the three-dimensional space, the direction passing through the origin and the lattice nodes nu,nv,nw, where n is an integer, has direction indices [uvw]. This corresponds to taking the coordinates of the first lattice node on that direction after the origin as direction indices. The indices [-u, -v and -w] identify the same direction as [uvw] simply observed from the opposite side.
When a primitive unit cell is used, the direction indices are all integer; they may instead be rational when a centred unit cell is adopted.