# Understanding Equivalent Wyckoff positions

I'm somewhat confused by the concept of Wyckoff positions in crystal structures. From Quantum Chemistry of Solids by Robert Evarestov, the definition of a Wyckoff position is "all the crystallographic orbits which have the same (not only isomorphic, but the same) site-symmetry group". I was okay with this, but he then went on to define equivalent Wyckoff positions as positions such that "equivalent sites have the same point-group symmetry and the same orientations of symmetry elements with respect to the lattice".

What I fail to understand is how the equivalent Wyckoff positions don't collapse to a single Wyckoff position, as they seem to meet the criteria of having the same site-symmetry. Is there a clear explanation of what distinguishes two Wyckoff positions enough to be equivalent, but not just a single position?

To clarify my question a little more, here is the specific example given in the text for the space group 136, also called P42/mnm or $D_{4h}^{14}$.

Pairs of Wyckoff positions a-b, f-g, and i-j have isomorphic site-symmetry groups ($D_{2h},C_{2v},\text{ and } C_s$ respectively). As is seen from the table, the pairs of points a-b and f-g not only have isomorphic, but also equivalent Wyckoff positions. The equivalent sites have the same point group symmetry and the same orientations of symmetry elements with respect to the lattice.

In the Wycoff notation equivalent positions are labelled consecutively $a, b, c\cdots$ starting with $a$ for the highest symmetry. A position 2f, for example, indicates two equivalent atoms at position given by symmetry f. For each space group a table of general and special positions can be made. This includes point symmetries, positions multiplicities and Wycoff symbols. The table below shows examples.