Platonic solid - dodecahedron, new surface topolgy proof

NCamero writes: Quanta magazine reports that a trio of mathematicians has resolved one of the most basic questions about the dodecahedron. The cube, tetrahedron, octahedron and icosahedron cannot have a straight path you could take that would eventually return you to your starting point without passing through any of the other corners. The dodecahedron can.