A definition of a conventional unit cell of a lattice is one that contains the same point group symmetries as the overall lattice and is the smallest such cell.
I can understand how a (infinite) lattice can have a point group symmetry about any lattice point such as rotational symmetry, mirror symmetry etc.
But I cannot see the same for a unit cell. Please can someone explain how we go about comparing the point group symmetries of a unit cell to that of an overall lattice? (e.g. what points do we use, for a cell what exactly is meant by a symmetry when most transformations move it from its original position etc...)
In this diagram their is a unit cell in green. This cell clearly shares a the symmetry of reflection through the line A with the lattice. However the lattice is also symmetric by reflection through the line B but the unit cell is not even though for the lattice it is a point group symmetry of one of the lattice points within the unit cell. I would therefore say that this unit cell and the lattice do not share the same symmetry and therefore this unit cell is not a conventional unit cell. I however know (/am pretty confident) that this is indeed a conventional unit cell, given the above definition I, however cannot cell how this holds and where my reasoning is wrong.