Unification and classification of two-dimensional crystalline patterns using orbifolds (Q2808939)

The authors consider a topological approach, via orbifolds, to the unification and the classification of two-dimensional crystalline patterns. Orbifold is a term which has been coined by Conway to designate a quotient space of the general plane (elliptic, flat, hyperbolic) factored by the isometries of the pattern. They outline the main features of orbifolds (cones, corners, handles, cross-caps) and then they characterize orbifold classes. Following this, they consider the problem of printing manifolds, and in this way they deal successively with point and plane groups on the one hand, and periodic groups on the other hand. The paper concludes with some comments on the transfer from orbifolds to space groups.