  Combining the microscopic Eilenberger theory with the first principles band
calculation, we investigate the stable flux line lattice (FLL) for a field
applied to the four-fold axis; $H\parallel [001]$ in cubic Nb. The observed FLL
transformation along $H_{c2}$ is almost perfectly explained without adjustable
parameter, including the tilted square, scalene triangle with broken mirror
symmetry, and isosceles triangle lattices upon increasing $T$. We construct a
minimum Fermi surface model to understand those morphologies, in particular the
stability of the scalene triangle lattice attributed to the lack of the mirror
symmetry about the Fermi velocity maximum direction in k-space.
