  The vertex corona of a vertex of some tiling is the vertex together with the
adjacent tiles. A tiling where all vertex coronae are congruent is called
monocoronal. We provide a classification of monocoronal tilings in the
Euclidean plane and derive a list of all possible symmetry groups of
monocoronal tilings. In particular, any monocoronal tiling with respect to
direct congruence is crystallographic, whereas any monocoronal tiling with
respect to congruence (reflections allowed) is either crystallographic or it
has a one-dimensional translation group. Furthermore, bounds on the number of
the dimensions of the translation group of monocoronal tilings in higher
dimensional Euclidean space are obtained.
