Z-monodromy diagrams

Z-monodromy M1 (o, circle).

Pankov and Tyc use the term z-monodromy to describe, in a triangulation, the connections that a zigzag makes external to the triangle under consideration. Mathematically a z-monodromy is a permutation on the 6 oriented edges of the triangle (3 edges x 2 orientations each.) For example, the identity permutation would indicate that each zigzag leaving from a given edge in a given direction returns along that same edge in the same direction (see the diagram for M1 above). A zigzag's connections internal to the triangle are simply corner-turnings, represented by the permutation D_F. They found that only four types of z-monodromies occur in a unicursal deltahedron, designated M1, M2, M3, and M4.

The trajectory in each diagrams actually represents two z-monodromies; one of the orientations has been distinguished with arrowheads.

Z-monodromy M2 (*, star).

Z-monodromy M3 (+, plus).

Z-monodromy M4 (-, minus).