Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability

Two 2D quasiperiodic tilings with generalized tenfold symmetry are derived from the lattice A 4 R , the reciprocal of the root lattice A 4 . Both tilings are built from four tiles, triangles in one case, rhombi and hexagons in the other. After a brief description of the tilings and their structures, the authors introduce the equivalence concept of mutual local derivability. They present its key properties and its application to several tenfold tilings and discuss some implications on a future classification of tilings in position space.