A regular octahedron is made up of eight equilateral triangles, each with side length one unit, as shown below. An ant starts at the top vertex, walks along the edges of the triangles without ever traversing the same edge twice, and ends at the top vertex. If she did not pass through the top vertex at any other point in her walk, how many units are in the maximum distance she could walk?
I don't really understand how I might approach this problem. Do I approach it with casework, or brute guessing?