The arrows etched onto the triangles form paths worming around the surface of the octahedron. The etched "START" and "END" words are indicating the edges where the important path starts and ends. (It's not as clear as I would like, but the intent is that, if you hit an edge from one face of the octagon, you must leave that edge onto the other face sharing that edge. The more strangely curving arrows indicate where the path can break this rule: the path is considered to have "hit" the edge that it passes by, on its way to hitting the next edge.)
Note also that the digits etched onto the pieces now form a two-digit number at each edge.