Add to ORKGAmmann bars are formed by segments (decorations) on the tiles of a tiling such that forming straight lines with them while tiling forces non-periodicity. Only a few cases are known, starting with Robert Ammann's observations on Penrose tiles, but there is no general explanation or construction. In this article we propose a general method for cut and project tilings based on the notion of subperiods and we illustrate it with an aperiodic set of 36 decorated prototiles related to what we called Cyrenaic tilings.Comment: sagemath code as an ancillary fil
In 1982 a quasi-crystal with 5-fold rotational symmetry was discovered by Shechtman et al. The most ...
This paper introduces two tiles whose tilings form a one-parameter family of tilings which can all b...
ABSTRACT. Wang tiles are square unit tiles with colored edges. A finite set of Wang tiles is a valid...
International audienceThis paper introduces two tiles whose tilings form a one-parameter family of t...
In this article we study Ammann tilings from the perspective of symplectic geometry. Ammann tilings ...
AbstractQuasiperiodic tilings are those tilings in which finite patterns appear regularly in the pla...
We give a simple set of two tiles that can only tile aperiodically | that is no tiling with these ti...
International audienceAperiodic tilings are non-periodic tilings characterized by local constraints....
Aperiodic tilings are interesting to mathematicians and scientists for both theoretical and practica...
In the 1960’s and 1970’s, mathematicians discovered geometric patterns which displayed a high degree...
We give an alternative simple proof that the monotile introduced by Smith, Myers, Kaplan and Goodman...
An n-dimensional tiling is formed by laying tiles, chosen from a finite collection of shapes (protot...
AbstractWe give a simple set of two tiles that can only tile aperiodically—that is no tiling with th...
International audienceWe establish a structure theorem for the family of Ammann A2 tilings of the pl...
5 pages, 1 figureIcosahedral tilings, although non-periodic, are known to be characterized by their ...
In 1982 a quasi-crystal with 5-fold rotational symmetry was discovered by Shechtman et al. The most ...
This paper introduces two tiles whose tilings form a one-parameter family of tilings which can all b...
ABSTRACT. Wang tiles are square unit tiles with colored edges. A finite set of Wang tiles is a valid...
International audienceThis paper introduces two tiles whose tilings form a one-parameter family of t...
In this article we study Ammann tilings from the perspective of symplectic geometry. Ammann tilings ...
AbstractQuasiperiodic tilings are those tilings in which finite patterns appear regularly in the pla...
We give a simple set of two tiles that can only tile aperiodically | that is no tiling with these ti...
International audienceAperiodic tilings are non-periodic tilings characterized by local constraints....
Aperiodic tilings are interesting to mathematicians and scientists for both theoretical and practica...
In the 1960’s and 1970’s, mathematicians discovered geometric patterns which displayed a high degree...
We give an alternative simple proof that the monotile introduced by Smith, Myers, Kaplan and Goodman...
An n-dimensional tiling is formed by laying tiles, chosen from a finite collection of shapes (protot...
AbstractWe give a simple set of two tiles that can only tile aperiodically—that is no tiling with th...
International audienceWe establish a structure theorem for the family of Ammann A2 tilings of the pl...
5 pages, 1 figureIcosahedral tilings, although non-periodic, are known to be characterized by their ...
In 1982 a quasi-crystal with 5-fold rotational symmetry was discovered by Shechtman et al. The most ...
This paper introduces two tiles whose tilings form a one-parameter family of tilings which can all b...
ABSTRACT. Wang tiles are square unit tiles with colored edges. A finite set of Wang tiles is a valid...