The generalized bug problem. How do you solve it?

>you have a 3D block whose dimensions are A*B*C which can be any numbers unlike in picrelated where they're A=1, B=1 and C=2
>bug starts at one of the vertices
>you choose a point anywhere on the surface of the block
>the bug takes the shortest possible route to that point
>you always choose the point such that it forces the bug to walk the longest possible distance
>what is that distance in terms of the variables A, B and C?