Cube cross-sections

Play with the cross-sections of a cube. Can it be an equilateral triangle? How about a square? Rectangle that is not a square? Regular hexagon? Pentagon (not necessarily regular)? Octagon? If it can, describe the situation. Point X moves along the x axis. Point ZX moves freely in the xz plane. Point XY moves freely in the xy plane or can be lifted by double clicking. Right click and drag to orbit the cube.