The Spectre tiling and all Spectre-like tilings have pure point diffraction and are MLD to reprojections of a cut-and-project model set, with the smallest possible first Čech cohomology.
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On the long-range order of the Spectre tilings
The Spectre tiling and all Spectre-like tilings have pure point diffraction and are MLD to reprojections of a cut-and-project model set, with the smallest possible first Čech cohomology.