Theory:
Figure 2.16. A geodesic intersecting itself on a 90 cone.
http://www.math.cornell.edu/~dwh/books/eg99/Ch02/Ch02.html
Figure 11.5. Self-intersections on a cone with angle f.
http://www.math.cornell.edu/~dwh/books/eg99/Ch11/Ch11.html
http://igkt.net/sm/index.php?topic=5030.msg33166#msg33166
Practical application: