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*)



A terminological question concerning orbifolds. 
Take a look at Thurston's notes (Chapter 13 of his "The geometry and topology of 3-manifolds", available at the MSRI's site: <http://library.msri.org/books/gt3m/>). Thurston calls these points *singular points*. (Same as Satake in his original paper "The Gauss-Bonnet Theorem for V-manifolds" from 1957 where he introduces orbifolds, under the name *V-manifolds*, see [Link](https://projecteuclid.org/journals/journal-of-the-mathematical-society-of-japan/volume-9/issue-4/The-Gauss-Bonnet-Theorem-for-V-manifolds/10.2969/jmsj/00940464.full)) As a geometric topologist, I would use Satake-Thurston's terminology. However, they both work in the geometric topology/Riemannian geometry setting. In the algebro-geometric context you could call them *orbifold points* to distinguish these points from singular point of the underlying variety.


Google search revealed the following statistics: "stacky point": 328 hits,
"orbifold point": 9,750 hits, "singular point" + orbifold: 17,500 hits.


I also like "stucky" and "sticky" points: If you have an isolated singular point $p$ of a Riemannian orbifold, then unparameterized geodesics after entering $p$ get "stuck" there.


On even lighter note, Thurston in his notes explains that the name "orbifold" is the result of a vote he had at his seminar in Princeton. One can have a similar vote on MO to determine what to call points with nontrivial stabilizer.


