Crystallographic groups

Crystallographic groups are mathematical classifications that describe how a crystal's structure repeats in space. They combine symmetry operations, like rotations and reflections, to represent the ways a crystal can be transformed without changing its overall structure. Each group corresponds to specific arrangements of atoms, influencing the crystal's properties. In essence, crystallographic groups help scientists understand and predict how materials behave based on their internal arrangement, which is crucial in fields like chemistry, physics, and materials science.