  Crystallographic tilings of the Euclidean space $\mathbb{E}^n$ are defined as
simple tilings whose group of isometric automorphisms is crystallographic. To
classify crystallographic tilings by their automorphism groups it is necessary
to extend the standard equivalence relation of mutual local derivability to a
version taking more general isometries than translations into account. This
also requires the extension of the standard metrics on tiling spaces. Finally,
a tiling with a given crystallographic group as automorphism group is
constructed.
