= Crystallographic site multiplicity
{title2=$m$}
\b[Crystallographic site multiplicity] is the number of distinct equivalent positions generated from one representative site by the <space group> within the conventional <unit cell>. It is a property of the <Wyckoff position>. If the <site-symmetry group> leaves a representative position fixed, fewer distinct positions are generated than at a general site.<Atom-site symmetry and disorder in the IUCr core CIF dictionary>[`_atom_site_site_symmetry_multiplicity`, Definition]{ref}
The relation can be written
$$
m=\frac{m_{\mathrm{general}}}{|G_{\mathrm{site}}|},
$$
where $m_{\mathrm{general}}$ is the general-position multiplicity and $|G_{\mathrm{site}}|$ is the order of the site-symmetry group. For an original compatible example, general multiplicity8 and site-symmetry order2 give $m=4$.
Multiplicity is distinct from <crystallographic site occupancy> $q$. For one atom type represented at equivalent positions, its average contribution to the atom count per unit cell is
$$
N=mq.
$$
A multiplicity8 site occupied to0.25 contributes2 atoms per cell on average. A fully occupied multiplicity4 site contributes4. If these are separate inequivalent sites for the same element, their total contribution is6.
Full occupancy at a symmetry-special site is still $q=1$, rather than automatically a fractional value. The symmetry reduction is already counted by $m$. Dividing occupancy again by the site-symmetry order would count that reduction twice. These distinctions connect a list of representative coordinates to the chemical contents of the unit cell.
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