Abstract: Two confusing points in teaching of crystal and on many current textbooks are concerned. Lattice transformation is used to infer whether the formation being a new Bravais lattices or not and additional constraint is added to four indices. The lattice transformation must be carried out in same crystal system, and the transformation into another crystal system could not deny the original lattice. Three methods are provided to prove that the additional constraint in four indices has a rigorous mathematical foundation. This is favorable for students to understand the related contents in crystal structures.

Key words: crystal structure, lattice transformation, four indices