Sections of a cube
This interactive animation shows the various polygons that can be obtained by cutting a cube with a plane. Three privileged directions are put in evidence (buttons on the left in the bottom): a plane perpendicular to the line that goes through the centres of opposite faces, a plane perpendicular to the line which goes through the midpoints of opposite edges, a plane perpendicular to the line which goes through opposite vertices. You can also move the cube with a small orange crank on the lines. You can rotate the cube (with a click and drag) in different positions.
Another animation shows the analogous situation on a hypercube.
animazione di Gian Marco Todesco