 Fractional crystal coordinate

Fractional crystal coordinates are the dimensionless coefficients in $r=u{a}_1+v{a}_2+w{a}_3$ 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.