# On inflation rules for Mosseri–Sadoc tilings

@article{Papadopolos1999OnIR,
title={On inflation rules for Mosseri–Sadoc tilings},
author={Zorka Papadopolos and Oleg Ogievetsky},
journal={Materials Science and Engineering A-structural Materials Properties Microstructure and Processing},
year={1999},
pages={385-388}
}
• Published 3 November 1999
• Mathematics
• Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
3 Citations
• Mathematics
Discret. Comput. Geom.
• 2001
The Dehn invariants of the Mosseri—Sadoc tiles provide two eigenvectors of the inflation matrix with eigenvalues equal to \t = (1+\sqrt 5 )/2 and -1/\t , and allow us to reconstruct theflation matrix uniquely.
• Mathematics
Acta crystallographica. Section A, Foundations and advances
• 2021
It is shown that the 3D Euclidean space can be tiled face-to-face with maximal face coverage by the composite tiles with an inflation factor τ generated by an inflation matrix.

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We derive the class of quasiperiodic tilings due to Mosseri and Sadoc, denoted by , from the quasiperiodic tilings of Kramer et al., obtained by icosahedral projection from the 6-dimensional root
• Mathematics
Discret. Comput. Geom.
• 2001
The Dehn invariants of the Mosseri—Sadoc tiles provide two eigenvectors of the inflation matrix with eigenvalues equal to \t = (1+\sqrt 5 )/2 and -1/\t , and allow us to reconstruct theflation matrix uniquely.
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This survey develops some aspects of this embedding for centered hypercubic 6D lattices and hopes to show that the 3D sections of this lattice display a rich geometric structure which they expect to encounter in the geometry and physics of the corresponding quasicrystals.

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