an orbifold is defined as "a space obtained by identifications that have fixed points" I am working on a problem that gives a circle C -1 <= x < =1 identified by x ~ x+2 with fundamental domain -1 < x <= 1. This is not an orbifold, right, even though -1 and 1 are identified on the circle? The problem then has C/Z_2 where Z_2 is the identification defined as usual x ~ -x. Obviously it has a fixed point at x = 0. I am confused about the question: "define the action of this (the Z_2) identification on the circle" Does this mean find you take the union of all identified points or the intersection? The problem also says that there are two fixed points. How? I can only think of x = 0?