= Wyckoff position
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A \b[Wyckoff position] of a <space group> consists of all points whose <site-symmetry groups> are <conjugate subgroups> of that space group. It classifies sites by their symmetry relationship within the whole group. A <Wyckoff letter> labels each such class in the conventional tables; the label is accompanied by its <crystallographic site multiplicity>.<Site symmetry and Wyckoff positions in the IUCr Online Dictionary of Crystallography>[Wyckoff position, Definition]{ref}
A <Wyckoff position> need not specify one particular atom or one fixed coordinate triplet. A general position usually has free fractional parameters. Choosing those parameters produces a <crystallographic orbit>, the collection of equivalent sites generated from that choice by the <space group>. Different parameter choices can give distinct orbits belonging to the same <Wyckoff position>.
An original comparison uses $P\bar1$, with operations $\mathbf r\mapsto\pm\mathbf r+\mathbf n$, where $\mathbf n$ is a lattice vector. Generic positions form pairs $\{\mathbf r,-\mathbf r\}$ modulo lattice translations and have trivial <site-symmetry groups>. Many different pairs therefore belong to the same general <Wyckoff position>.
The origin and the half-cell point $(1/2,0,0)$ instead each have an inversion-containing <site-symmetry group> of order2. Their groups are isomorphic but not conjugate within this <space group>: a group operation sends the origin to an integer lattice point, never to that half-cell point. They occupy different special <Wyckoff positions>. Group order or multiplicity alone therefore does not uniquely identify a <Wyckoff position>.
This classification helps constrain independent atomic coordinates in a <crystal structure>; it describes allowed symmetry, not which chemical species occupies a site or its fractional occupation.
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