The notion of orbifold is quite well established by now. I would like to ask how one should call a point of an orbifold with non-trivial stabilizer? Should one call this *a singular point*? Of something else?

For some reason, I was not able to find any text that fixes this innocent bit of terminology concerning orbifolds.

*Comment.* I would like to stress, that I want to know how to call A point (i.e. one point) that has a non-trivial stabilizer. Indeed, as Ryan says in his comment, there is some terminology to define the union of all points with non-trivial stabilizer, but this is not what I am looking for (for example, in algebraic geometry there is a canonical way to call a point that is not smooth, it is called *a singular point*)

singular point, since "singular point" already has a well established meaning on an algebraic variety. Moreover, it suggests misleadingly that the presence of nontrivial isotropy causes the stack to become singular, when morally it is the other way around... the coarse moduli space has no orbifold points, but will in general acquire singularities to compensate. – Dan Petersen Apr 18 '12 at 6:30