2026/04/05 by Rehab Al Raisi, Nazife Ozdes Koca, Mehmet Koca +1 · 1 voice
Physics and Astronomy · #cond-mat.other #math-ph
arxiv published 2026/04/05 · arxiv updated 2026/04/16
A modified set of Mosseri-Sadoc (MS) tiles tessellating 3D Euclidean space with icosahedral symmetry is introduced. The new set of tiles are embedded in dodecahedron with a threefold symmetric order. The modified Mosseri-Sadoc (MMS) tiles can be inflated by a new inflation matrix with positive eigenvalues τ3 and τ with the corresponding eigenvectors representing the volumes and the Dehn invariants of the tiles, respectively, where τ=(1+√5)/(2) is the golden ratio. The MMS tiles are obtained by projection of the 4D and 5D facets of the Delone cells tiling the D6 root lattice in an alternating order. It is also proved that a subset of the lattice D6 projects into the dodecahedron inflated by τn with an arbitrary integer n and tiled by the MMS tiles.