two and three dimensional lattice
Answers
The most general and least symmetric Bravais lattice in two dimensions is the oblique lattice. If the angle between the two lattice vectors is 90°, the higher symmetry of the cell gives rise to a distinct Bravais lattice, either rectangular or square depending on whether the unit cell vectors have different length or not. In the case of a rectangular lattice, we can distinguish between a primitive rectangular lattice and a centred rectangular lattice, which has an extra lattice point (atom) at the centre. The centred rectangular lattice could be set up as a primitive lattice with lower symmetry (unit cell shown in green), but convention prefers the more symmetric description. Finally, if the lattice vectors are the same length and the angle is 120°, we have another special case with higher symmetry, the hexagonal lattice.