Plane application of orbifold classification
Baynard, William Thorn, III
The classification of objects and tilings of the plane through symmetry is an algebraic application used in chemistry, physics, and mathematics. In 1992, John H. Conway and William P. Thurston formulated a classification system based on the geometric notion of an "orbifold". The sophisticated orbifold approach to analyzing symmetry resulted in an elegant, more simplified classification scheme. The following is an exposition of the orbifold classification system with application to the well known 17 plane crystallographic groups.
Orbifolds; Crystallography -- Classification