Symmetries of Monocoronal Tilings
Dirk Frettlöh, Alexey Garber
Abstract
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.
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