Is it possible to know the entire configuration of a Rubik's cube looking at only two sides and not rotating the cube? In other words: what is the minimum information required to create a two-dimensional map of a $3\times 3\times 3$ Rubik's cube?
Take a solved cube and flip all four edges with a red face. Now you can permute those edges freely without the effect being visible on any other side than the one with the red center. So even seeing five sides of the cube is not enough to reconstruct the last one.
(And by "freely" I mean that any even permutation of the edges can be reached by legal cube moves, of course).
If you look at two opposite sides and they are solid colors, you can't distinguish rotations of the other sides.
Since you can see two sides, you can see, in total, 6 out of the 8 corners. By twisting the two you can't see in opposite directions, you can change the orientation of these corners while having a cube that can still be solvable.