23 citations · 120 across the 28 of their papers we have counts for
4 papers · 1 filter
Shield tilings
Thomas Fernique, Olga Mikhailovna Sizova
We provide a complete description of the edge-to-edge tilings with a regular triangle and a shield-shaped hexagon with no right angle. The case of a hexagon with a right angle is a…
Icosahedral Tilings Revisited
Nicolas Bédaride, Thomas Fernique
Icosahedral tilings, although non-periodic, are known to be characterized by their configurations of some finite size. This characterization has also been expressed in terms of a s…
The Ammann-Beenker tilings revisited
Nicolas Bédaride, Thomas Fernique
This paper introduces two tiles whose tilings form a one-parameter family of tilings which can all be seen as digitization of two-dimensional planes in the four-dimensional Euclide…
Combinatorial substitutions and sofic tilings
Thomas Fernique, Nicolas Ollinger
A combinatorial substitution is a map over tilings which allows to define sets of tilings with a strong hierarchical structure. In this paper, we show that such sets of tilings are…