Question 24
A solid regular tetrahedron has 4 faces, each an equilateral triangle. It is suspended in the entomology laboratory. There are two food sources on the tetrahedron, one at a vertex $V$ and the other at $X$, the centre of the opposite face. When a geodesic grub is placed anywhere upon the tetrahedron, it instinctively crawls along the shortest possible path over the surface to the closest food source. What fraction of the surface area is closer to $V$ than to $X$, in terms of paths along the surface?
