Modified Mosseri-Sadoc tiles from $D_6$
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914478628536320 |
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| author | Raisi, Rehab Al Koca, Nazife Ozdes Koca, Mehmet Koc, Ramazan |
| author_facet | Raisi, Rehab Al Koca, Nazife Ozdes Koca, Mehmet Koc, Ramazan |
| contents | 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 $τ^3$ and $τ$ with the corresponding eigenvectors representing the volumes and the Dehn invariants of the tiles, respectively, where $τ=\frac{1+\sqrt5}{2}$ is the golden ratio. The MMS tiles are obtained by projection of the 4D and 5D facets of the Delone cells tiling the $D_6$ root lattice in an alternating order. It is also proved that a subset of the lattice $D_6$ projects into the dodecahedron inflated by $τ^n$ with an arbitrary integer $n$ and tiled by the MMS tiles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03988 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modified Mosseri-Sadoc tiles from $D_6$ Raisi, Rehab Al Koca, Nazife Ozdes Koca, Mehmet Koc, Ramazan Other Condensed Matter Mathematical Physics 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 $τ^3$ and $τ$ with the corresponding eigenvectors representing the volumes and the Dehn invariants of the tiles, respectively, where $τ=\frac{1+\sqrt5}{2}$ is the golden ratio. The MMS tiles are obtained by projection of the 4D and 5D facets of the Delone cells tiling the $D_6$ root lattice in an alternating order. It is also proved that a subset of the lattice $D_6$ projects into the dodecahedron inflated by $τ^n$ with an arbitrary integer $n$ and tiled by the MMS tiles. |
| title | Modified Mosseri-Sadoc tiles from $D_6$ |
| topic | Other Condensed Matter Mathematical Physics |
| url | https://arxiv.org/abs/2604.03988 |