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We give the inflation rules for the decorated Mosseri–Sadoc tiles in the projection class of tilings T (M S). Dehn invariants related to the stone inflation of the Mosseri–Sadoc tiles provide eigenvectors of the inflation matrix with eigenvalues equal to τ = 1+ √ 5 2 and (−τ −1).
We introduce Dehn invariants as a useful tool in the study of the inflation of quasiperiodic space tilings. The tilings by " golden tetrahedra " are considered. We discuss how the Dehn invariants can be applied to the study of inflation properties of the six golden tetrahedra. We also use geometry of the faces of the golden tetrahedra to analyze their… (More)
Tiles–inflation rules for the class of canonical tilings T * (2F) derived by the projection method Abstract The tiles of the canonical tilings T * (2F) are six tetrahedra. We determine their inflation rules by the projection method.