Trajectory on a Polyhedron from a Vertex to Itself
Given a net for a polyhedron, find a straight line from some vertex to itself that lies inside the net. For the regular dodecahedron, such a line exists that does not pass through any other vertex . In this Demonstration, a random net for a polyhedron is given. Drag the locators at the two ends of the red line to try to join the vertex to itself.