On the definition and classification of Bravais lattices

The number of Bravais lattices (or lattice types) in three-dimensional space is well known to be 14 if, as is usual, a lattice type is defined as the class of all simple lattices whose lattice groups (that is, arithmetic holohedries) belong to the same conjugacy class in GL(3, Z). However, it is also common in the literature to introduce the lattice types using the original point of view of Bravais (and Cauchy), according to which a type collects all the lattices that can be connected by a continuous deformation along which the lattice symmetry does not decrease. It is shown that these two definitions are in fact nor equivalent. Bravais' own criterion results in only 11 lattice types.