Fibrifold
In mathematics, a fibrifold is a fiber space whose fibers and base spaces are orbifolds. They were introduced by, 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.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 | Hextetrahedral
*332 | Gyroidal
432 | Diploidal
3*2 | Tetartoidal
332 |
| bc lattice | 8o:2 | 4o:2 | 8+o | 8−o | 4oo |
| nc lattice | 4−:2 | 2o:2 | 4−o | 4− | 2o |
| nc lattice | 4+:2 | 2o:2 | 4+ | 4+o | 2o |
| fc lattice | 2−:2 | 1o:2 | 2−o | 2− | 1o |
| fc lattice | 2+:2 | 1o:2 | 2+ | 2+o | 1o |
Other
lattice
groups | 8o
8oo
4− −
4++ | 4o
2oo | | | |
Achiral
quarter
groups | 8o/4 | 4o/4 | 4+/4
2+/4 | 2−/4
4−/4 | 1o/4
2o/4 |
Irreducible group symbols in Hermann–Mauguin notation, Fibrifold notation, geometric notation, and Coxeter notation:
