In crystallography there are conventions as to how the indices of planes and directions are written. When referring to a specific plane, "round" brackets are used:
(hkl)
When referring to a set of planes related by symmetry, then "curly" brackets are used:
{hkl}
These might be the (100) type planes in a cubic system, which are (100), (010), (001), (00),(00) and (00) . These planes all "look" the same and are related to each other by the symmetry elements present in a cube, hence their different indices depend only on the way the unit cell axes are defined. That is why it useful to consider the equivalent (010) set of planes.
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Directions in the crystal can be labelled in a similar way. These are effectively vectors written in terms of multiples of the lattice vectors a, b, and c. They are written with "square" brackets:
[UVW]
A number of crystallographic directions can also be symmetrically equivalent, in which case a set of directions are written with "triangular" brackets:
<UVW>
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