In the first example, we start with a 60° periodicity cell (hexagonal periodicity) and maximize the shear modulus of the homogenized material. The optimization algorithm changes the periodicity cell to a 45° parallelogram.

In the second example, we start with square periodicity and maximize the Young modulus of the homogenized material along a direction with slope 30°. The optimization algorithm changes the periodicity cell to a rectangle with slope 30°.