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An Introduction to Orbifolds

These pages are loosely based on a talk titled "Symmetries, Lattices, and Tilings" given by John Conway at the Regional Geometry Institute at Smith College on July 12, 1993, funded by NSF grant #DMS-90 13220.

Introduction
Orbifolds of plane patterns
Orbifolds of spherical patterns
Other features: handles and cross caps
Why there are Finitely many Plane and Sphere Patterns
Paying for Sphere Patterns
Why it works
Conclusion
Exercises
Supplemental materials
- Examples of orbifolds of plane patterns
- Video: Not Knot

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