I am not sure how to proceed on exercise 3.2.3 in Thurston's book "Three Dimensional Geometry and Topology". The wording is as follows: "In a gluing of three dimensional simplices, each edge enters into exactly two gluings, one for each of its faces. Composing these, one gets a cycle of gluings that eventually must return to the original edge. Suppose that the composition of gluings around the cycle reverses the edge's orientation. Describe a neighborhood of the fixed point of the return map of the edge to itself, in the resulting identification space."
I am having difficulty visualizing what happens to the faces or how one would say anything explicit. Does anyone have any intuition for this? Any help is much appreciated.