Английская Википедия:Fibrifold
Материал из Онлайн справочника
In mathematics, a fibrifold is (roughly) a fiber space whose fibers and base spaces are orbifolds. They were introduced by Шаблон:Harvs, who introduced a system of notation for 3-dimensional fibrifolds and used this to assign names to the 219 affine space group types. 184 of these are considered reducible, and 35 irreducible.
Irreducible cubic space groups
The 35 irreducible space groups correspond to the cubic space group.
8o:2 | 4−:2 | 4o:2 | 4+:2 | 2−:2 | 2o:2 | 2+:2 | 1o:2 | |||
8o | 4− | 4o | 4+ | 2− | 2o | 2+ | 1o | |||
8o/4 | 4−/4 | 4o/4 | 4+/4 | 2−/4 | 2o/4 | 2+/4 | 1o/4 | |||
8−o | 8oo | 8+o | 4− − | 4−o | 4oo | 4+o | 4++ | 2−o | 2oo | 2+o |
Class Point group |
Hexoctahedral *432 (mШаблон:Overlinem) |
Hextetrahedral *332 (Шаблон:Overline3m) |
Gyroidal 432 (432) |
Diploidal 3*2 (mШаблон:Overline) |
Tetartoidal 332 (23) |
---|---|---|---|---|---|
bc lattice (I) | 8o:2 (ImШаблон:Overlinem) | 4o:2 (IШаблон:Overline3m) | 8+o (I432) | 8−o (IШаблон:Overline) | 4oo (I23) |
nc lattice (P) | 4−:2 (PmШаблон:Overlinem) | 2o:2 (PШаблон:Overline3m) | 4−o (P432) | 4− (PmШаблон:Overline) | 2o (P23) |
4+:2 (PnШаблон:Overlinem) | 4+ (P4232) | 4+o (PnШаблон:Overline) | |||
fc lattice (F) | 2−:2 (FmШаблон:Overlinem) | 1o:2 (FШаблон:Overline3m) | 2−o (F432) | 2− (FmШаблон:Overline) | 1o (F23) |
2+:2 (FdШаблон:Overlinem) | 2+ (F4132) | 2+o (FdШаблон:Overline) | |||
Other lattice groups |
8o (PmШаблон:Overlinen) 8oo (PnШаблон:Overlinen) 4− − (FmШаблон:Overlinec) 4++ (FdШаблон:Overlinec) |
4o (PШаблон:Overline3n) 2oo (FШаблон:Overline3c) |
|||
Achiral quarter groups |
8o/4 (IaШаблон:Overlined) | 4o/4 (IШаблон:Overline3d) | 4+/4 (I4132) 2+/4 (P4332, P4132) |
2−/4 (PaШаблон:Overline) 4−/4 (IaШаблон:Overline) |
1o/4 (P213) 2o/4 (I213) |
Файл:Cubic space group lattices.png | Файл:Tetragonal disphenoid symmetry0.png | Файл:Quadrilateral tree.png |
8 primary hexoctahedral hextetrahedral lattices of the cubic space groups | The fibrifold cubic subgroup structure shown is based on extending symmetry of the tetragonal disphenoid fundamental domain of space group 216, similar to the square |
Irreducible group symbols (indexed 195−230) in Hermann–Mauguin notation, Fibrifold notation, geometric notation, and Coxeter notation:
References