Coxeter Groups as Automorphism Groups of Solid Transitive 3-simplex Tilings
Апстракт
In the papers of I. K. Zhuk, then more completely of E. Molnar, I. Prok, J. Szirmai all simplicial 3-tilings have been classified, where a symmetry group acts transitively on the simplex tiles. The involved spaces depends on some rotational order parameters. When a vertex of a such simplex lies out of the absolute, e. g. in hyperbolic space H-3, then truncation with its polar plane gives a truncated simplex or simply, trunc-simplex. Looking for symmetries of these tilings by simplex or trunc-simplex domains, with their side face pairings, it is possible to find all their group extensions, especially Coxeter's reflection groups, if they exist. So here, connections between isometry groups and their supergroups is given by expressing the generators and the corresponding parameters. There are investigated simplices in families F3, F4, F6 and appropriate series of trunc-simplices. In all cases the Coxeter groups are the maximal ones.
Кључне речи:
hyperbolic space group / fundamental domain by simplex and trunc-simplex / Coxeter groups as supergroupsИзвор:
Filomat, 2014, 28, 3, 557-577Издавач:
- Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
DOI: 10.2298/FIL1403557S
ISSN: 0354-5180
WoS: 000343240900013
Scopus: 2-s2.0-84904394111
Институција/група
Fakultet organizacionih naukaTY - JOUR AU - Stojanović, Milica PY - 2014 UR - https://rfos.fon.bg.ac.rs/handle/123456789/1247 AB - In the papers of I. K. Zhuk, then more completely of E. Molnar, I. Prok, J. Szirmai all simplicial 3-tilings have been classified, where a symmetry group acts transitively on the simplex tiles. The involved spaces depends on some rotational order parameters. When a vertex of a such simplex lies out of the absolute, e. g. in hyperbolic space H-3, then truncation with its polar plane gives a truncated simplex or simply, trunc-simplex. Looking for symmetries of these tilings by simplex or trunc-simplex domains, with their side face pairings, it is possible to find all their group extensions, especially Coxeter's reflection groups, if they exist. So here, connections between isometry groups and their supergroups is given by expressing the generators and the corresponding parameters. There are investigated simplices in families F3, F4, F6 and appropriate series of trunc-simplices. In all cases the Coxeter groups are the maximal ones. PB - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš T2 - Filomat T1 - Coxeter Groups as Automorphism Groups of Solid Transitive 3-simplex Tilings EP - 577 IS - 3 SP - 557 VL - 28 DO - 10.2298/FIL1403557S UR - conv_1663 ER -
@article{ author = "Stojanović, Milica", year = "2014", abstract = "In the papers of I. K. Zhuk, then more completely of E. Molnar, I. Prok, J. Szirmai all simplicial 3-tilings have been classified, where a symmetry group acts transitively on the simplex tiles. The involved spaces depends on some rotational order parameters. When a vertex of a such simplex lies out of the absolute, e. g. in hyperbolic space H-3, then truncation with its polar plane gives a truncated simplex or simply, trunc-simplex. Looking for symmetries of these tilings by simplex or trunc-simplex domains, with their side face pairings, it is possible to find all their group extensions, especially Coxeter's reflection groups, if they exist. So here, connections between isometry groups and their supergroups is given by expressing the generators and the corresponding parameters. There are investigated simplices in families F3, F4, F6 and appropriate series of trunc-simplices. In all cases the Coxeter groups are the maximal ones.", publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš", journal = "Filomat", title = "Coxeter Groups as Automorphism Groups of Solid Transitive 3-simplex Tilings", pages = "577-557", number = "3", volume = "28", doi = "10.2298/FIL1403557S", url = "conv_1663" }
Stojanović, M.. (2014). Coxeter Groups as Automorphism Groups of Solid Transitive 3-simplex Tilings. in Filomat Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 28(3), 557-577. https://doi.org/10.2298/FIL1403557S conv_1663
Stojanović M. Coxeter Groups as Automorphism Groups of Solid Transitive 3-simplex Tilings. in Filomat. 2014;28(3):557-577. doi:10.2298/FIL1403557S conv_1663 .
Stojanović, Milica, "Coxeter Groups as Automorphism Groups of Solid Transitive 3-simplex Tilings" in Filomat, 28, no. 3 (2014):557-577, https://doi.org/10.2298/FIL1403557S ., conv_1663 .