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An ** orbifold** is a Hausdorff space which is locally
homeomorphic at each point to , where
is some finite group, perhaps different for different .
The set of s.t. (in other words, points
no neighborhood of which is homeomorphic to ) is called the
** singular locus** of the orbifold .

An orbifold is called ** good** if it has a covering which is a manifold.

The following amazing theorem is true for 2-orbifolds:

The singular locus of a 2-orbifold has only three possible types of local model:

- A mirror , where acts by reflections along the line.
- A cone point of order acting by rotations of order .
- A corner reflection of order generated by all reflections in two lines which meet at an angle .

Here is an example which shows some of the features a 2-orbifold may have:

Wed Aug 24 16:29:50 CDT 1994