Symmetry in physics is not just about orientations in space. This notion rather comes from the fact that large systems of discrete points are often described us

Symmetry in physics is not just about orientations in space. This notion rather comes from the fact that large systems of discrete points are often described using continuum mechanics or field theory, which naturally has a lot more symmetries. But even a set of randomly distributed point-like particles can have symmetries. If the set was made up of identical bosons for example, it would have a wave function symmetry under particle permutations. And real particles would also exhibit a whole lot of other discrete symmetries, like CPT symmetry at the very least.