Brilli the ant is trapped on a cube-shaped planet. She wants to go from one corner [point] to the opposite corner [point ]. However she wants do this in a way such that she has to cross the shortest distance possible. If the length of the sides of the cube is , the shortest distance between and can be expressed as where and are non-negative integers and is square-free. What is ?
Details and assumptions:
Brilli the ant is completely confined to the surface of the cube. She can't move inside or outside the cube.