We had a disagreement regarding 2D Bravais lattices during a lecture. The lecturer told us that a centered rectangle forms a Bravais lattice in 2D, but a centered parallelogram isn't:
We couldn't come up with a satisfying definition of a Bravais lattice though. It appears to be a lattice with certain periodic/translation/etc. symmetries; but intuitively, putting a dot in the center of a rectangle symmetry-wise has the same effect putting one in a parallelogram does. Why is the distinction then? So, our questions are:
- Does a centered rectangle form a Bravais cell? (Wikipedia lists it as one.)
- Does a centered parallelogram not? (Wikipedia doesn't list any.)
- Why, and/or why not?
Edit: The question (Is the centered parallelogram a Bravais-cell?) was in a test we discussed, so an exact answer to this is encouraged.