801 citations
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8 papers · 1 filter
Similarity versus Coincidence Rotations of Lattices
S. Glied, M. Baake
The groups of similarity and coincidence rotations of an arbitrary lattice L in d-dimensional Euclidean space are considered. It is shown that the group of similarity rotations con…
Homometric Point Sets and Inverse Problems
Uwe Grimm, Michael Baake
The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, t…
The Lonely Vertex Problem
D. Frettlöh, A. Glazyrin
In a locally finite tiling of n-dim Euclidean space by convex polytopes, each point of the space is either a vertex of at least two tiles, or no vertex at all.
Coincidence rotations of the root lattice
Michael Baake, Uwe Grimm, Manuela Heuer +1
The coincidence site lattices of the root lattice are considered, and the statistics of the corresponding coincidence rotations according to their indices is expressed in ter…
Self-dual tilings with respect to star-duality
Dirk Frettlöh
The concept of star-duality is described for self-similar cut-and-project tilings in arbitrary dimensions. This generalises Thurston's concept of a Galois-dual tiling. The dual til…
Homometric model sets and window covariograms
Michael Baake, Uwe Grimm
Two Delone sets are called homometric when they share the same autocorrelation or Patterson measure. A model set LAMBDA within a given cut and project scheme is a Delone set that i…