60.17 Wyckoff Positions

A Wyckoff position of a space group G is an equivalence class of points in Euclidean space, having stabilizers which are conjugate subgroups of G. Apart from a subset of lower dimension, which contains points with even bigger stabilizers, a Wyckoff position consists of a G-orbit of some affine subspace A. A Wyckoff position W therefore can be specified by a representative affine subspace A and its stabilizer subgroup. In CrystGap, a Wyckoff position W is represented as a record with the following components:

W.basis:

Basis of the linear space L parallel to A. This basis is also a basis of the intersection of L with the translation lattice of S.
Can be extracted with WyckoffBasis( W ).

W.translation:

W.translation is such that A = L + W.translation.
Can be extracted with WyckoffTranslation( W ).

W.stabilizer:

The stabilizer subgroup of any generic point in A.
Can be extracted with WyckoffStabilizer( W ).

W.class:

Wyckoff positions carry the same class label if and only if their stabilizers have point groups which are conjugate subgroups of the point group of S.
Can be extracted with WyckoffPosClass( W ).

W.spaceGroup:

The space group of which it is a Wyckoff position.
Can be extracted with WyckoffSpaceGroup( W ).

W.isWyckoffPosition:

A flag identifying the record as a Wyckoff position. It is set to true.
Can be tested with IsWyckoffPosition( W ).

W.operations:

The operations record of a Wyckoff position. It currently contains only a Print function.

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