= Fractional crystal coordinate
{title2=$(u,v,w)$}
<Fractional crystal coordinates> are the dimensionless coefficients in $r=ua_1+va_2+wa_3$ for specified <unit cell> vectors. They are not Cartesian lengths unless the vectors themselves are included. With primitive vectors, replacing $u,v,w$ by values differing by <integers> selects an equivalent position in another <unit cell>.
In the two-dimensional example under <crystal structure>, B has position $(0.65,0.55)$ in ordinary length coordinates, but <fractional crystal coordinates> $(0.65/2,0.55/1.5)=(13/40,11/30)$. Multiplying these coefficients by the two translation vectors recovers the drawn position. Reporting the axes is therefore part of reporting a structure.
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