  This paper develops geographic-style maps containing 2D lattices in all known
crystals parameterised by recent complete invariants. Motivated by rigid
crystal structures, lattices are considered up to rigid motion and uniform
scaling. The resulting space of 2D lattices is a square with identified edges
or a sphere without one point. The new continuous maps show all Bravais classes
as low-dimensional subspaces, visualise hundreds of thousands of real crystal
lattices from the Cambridge Structural Database, and motivate the development
of continuous and invariant-based crystallography.
