arXiv subjects

Reinhard Lück

Publications and source records attributed to Reinhard Lück.

2 recordsLinked to original sources

arXiv2008

Ten colours in quasiperiodic and regular hyperbolic tilings

Colour symmetries with ten colours are presented for different tilings. In many cases, the existence of these colourings were predicted by group theoretical methods. Only in a few cases explicit constructions were known, sometimes using combination of two-colour and five-colour symmetries. Here we present explicit constructions of several of the predicted colourings for the first time, and discuss them in contrast to already known colourings with ten colours.

math.CO↗

arXiv1997

Icosahedral coincidence rotations

The coincidence problem for three-dimensional discrete structures with icosahedral symmetry is reinvestigated. We present a parametric description of the coincidence rotations based on special quaternions, called icosian numbers. In particular, we give a characterization of the possible coincidence indices (Sigma-factors) and present a complete list of the possible rotations with Sigma < 100.

cond-mat↗