Zigzag walk

A tetrahedron with each 1-zigzag shown in a different color.

A zigzag walk, also called a k-zigzag, is a polygon (usually skew) formed by following the edges of a polyhedron in a particular way.

Definition

A k-zigzag is a polygon formed by following the edges of a polyhedron in a particular way. Starting from a particular vertex and edge the polygon follows that edge to another vertex. It then follows along the kth rightmost edge to the next vertex, and then follows along the kth leftmost edge, repeating this pattern of left and right turns until the path loops back on itself.

A 1-zigzag, that is a path alternating between the leftmost and rightmost possible edges, is also called a Petrie polygon or sometimes just a zigzag, and is integral in the construction of the Petrie dual.

See also

• Petrie dual

External links

• Wikipedia Contributors. "Petrie polygon".
• Weisstein, Eric W. "Petrie Polygon" at MathWorld.

Bibliography

• Coxeter, Harold Scott MacDonald; Moser, William Oscar Jules (1972). Generators and Relations for Discrete groups (4 ed.). Springer-Verlag. doi:10.1007/978-3-662-21946-1.
• McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space" (PDF). Discrete Computational Geometry (47): 449–478. doi:10.1007/PL00009304.