I am in a mess about certain points in crystal physics please help me out with these doubts.
1. In the process of rotoinversion,we first rotate the object about an axis and then invert it--where does the centre of symmetry come in here?
2. In the process of rotoinversion,we are rotating a particle (say)about the rotational axis and then inverting about a certain chosen point----where does the roto inversion axis come in here--what is it actually?
3. In roto inversion of a cube, we hold a cube along an axis passing through one of its diagonals, rotate it,then invert it using the centre of symmetry,
Howewer,there is no point in inverting it about its centre of symmetry,since we don't obtain any new configuration due to it--right?
4.For combinations of symmetry elements,we get a point group--what is this all about---how are symmetry elements combined and how are they related to eachother?