Slicing Solids with a Plane
The selected Platonic solid is displayed in the left panel. To rotate it in space, click and drag with the mouse.
The intersection of the plane with the solid (the slice) is shown as a red polygon on the surface of the solid. The intersection also appears in the right panel so you can see it even when the intersection is on the back side of the solid and hidden from view.
You can rotate the solid to examine the slice for any fixed plane, or you can move the plane while keeping the solid in place.
For example, how many different polygon shapes can be obtained by slicing a cube with a plane? How many different kinds of shapes can you make by slicing a tetrahedron with a plane?