  Bravais lattices are the most fundamental building blocks of crystallography.
They are classified into groups according to their translational, rotational,
and inversion symmetries. In computational analysis of Bravais lattices,
fulfilment of symmetry conditions is usually determined by analysis of the
metric tensor, using either a numerical tolerance to produce a binary (i.e. yes
or no) classification, or a distance function which quantifies the deviation
from an ideal lattice type. The metric tensor, though, is not scale-invariant,
which complicates the choice of threshold and the interpretation of the
distance function. Here, we quantify the distance of a lattice from a target
Bravais class using strain. For an arbitrary lattice, we find the
minimum-strain transformation needed to fulfil the symmetry conditions of a
desired Bravais lattice type; the norm of the strain tensor is used to quantify
the degree of symmetry breaking. The resulting distance is invariant to scale
and rotation, and is a physically intuitive quantity. By symmetrizing to all
Bravais classes, each lattice can be placed in a 14 dimensional space, which we
use to create a map of the space of Bravais lattices and the transformation
paths between them. A software implementation is available online under a
permissive license.
