A2. A large cube $\begin{gathered}E F G H \\ A B C D\end{gathered}$ stands with face $A B C D$ on the ground. The front face $A B F E$ is oriented to the south. Els cannot lift the cube but can tilt it such that one edge remains in place. So, for example, if she tilts the cube once to the east, face $B F G C$ will be on the ground and face $E F G H$ will be oriented to the east. Starting from the initial position

![](https://cdn.mathpix.com/cropped/2024_04_17_0b81ff2ef64511bfe8eeg-1.jpg?height=380&width=488&top_left_y=1398&top_left_x=1292)
she tilts the cube five times to the east, then five times to the north, then five times to the west, and finally five times to the south. The cube is then back in its original position, but the vertices may have changed places.

Give all the vertices that have returned to their original positions.
A2. If you tilt the cube four times in the same direction, the orientation of the vertices will be the same as before. Instead of five times in one direction, you can get by with one time in a direction. It is clear that with one tilt to the east, B and C remain in place, then to the north: C remains in place again, and so it stays. After four times, point $\mathrm{C}$ is back in place, and thus point $\mathrm{E}$, which is diagonally opposite $\mathrm{C}$, is also back in place. These are the only vertices, because another vertex, for example B, ends up in the position of $\mathrm{D}$ and thus all other vertices change places, with the exception, of course, of $\mathrm{C}$ and $\mathrm{E}$.