Isometry defines perfect balance
Three equal axes at 90° yield cubic, octahedral, and dodecahedral habits from a single geometric constraint.
Hexagonal axes create polar forms
One unique axis of three- or sixfold symmetry with three equal axes at 120° in the basal plane.
Three axes, none alike
Three perpendicular axes of unequal length produce rhombic prismatic and pyramidal habits.
Monoclinic breaks the orthogonal rule
One axis departs from perpendicular — the most common symmetry class observed in nature.