The relationship between reduced cells in a general Bravais lattice

It is shown that in a three-dimensional Bravais lattice at most 5 different cells based on the shortest three non-coplanar translations (Buerger cells) may exist. Their mutual relationship is found and two procedures are proposed to find all these cells if one of them is known. That cell which corresponds to the reduced quadratic form is indicated. For any of the 14 types of Bravais lattice the number of different Buerger cells is ascertained.