In mathematics, a fibrifold is (roughly) a fiber space whose fibers and base spaces are

orbifold In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space that is locally a finite group quotient of a Euclidean space. D ...

s. 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 In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that ...

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. Irreducible group symbols (indexed 195−230) in

Hermann–Mauguin notation In geometry, Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups. It is named after the German crystallographer Carl Hermann (who introduced it in 1928) and the French mineralogist ...

, Fibrifold notation, geometric notation, and

Coxeter notation In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, ...

References

* * * * Symmetry Finite groups Discrete groups {{geometry-stub