56th Ukrainian National Mathematical Olympiad, Third Round

Three edges go from each vertex of a cube. Every edge is a part of two sides. Let us look at the vertex $1$. It lies inside all "known" sides. Hence these three sides form an angle with vertex in $1$. Then three edges are $1$-$2$, $1$-$6$, and $1$-$8$. Now it is easy to understand that $6$ is opposite to $5$.