TITLE: What is an example of an orbifold which is not a topological manifold?
QUESTION [22 upvotes]: In Thurston's book The Geometry and Topology of Three-Manifolds it is proven that the underlying space of a two-dimensional orbifold is always a topological surface. 
Are there any easy examples of higher dimensional orbifolds whose underlying spaces are not topological manifolds?

REPLY [3 votes]: To give a compact version of Igor's example, consider the antipodal map in the tangent space of a round 3-sphere at a point.  This extends to an isometry of the 3-sphere with a pair of fixed points.  The quotient by the isometry is a manifold with two conical singularities which is not homeomorphic to a topological 3-manifold.