Cube symmetry/Rotation at diagonal axis/Plane equation for permuted points/Exercise

Let $W$ be the cube with the vertices $(\pm 1,\pm 1,\pm 1)$. Let $\phi$ be a rotation around $120$ degree around the space diagonal through $(1,1,1)$ and $(-1,-1,-1)$. Determine the plane equations for those planes that are determined by three vertices that are moved to each other by this rotation.

Create a solution