A square within a square is a 2-D representation of a 3-D cube. (Roll Over)
By analogy a cube within a cube is a 3-D representation of a 4-d cube.(Roll Over)
A hyper cube made of reflective material seen from the inside. (Roll Over)
The simplified Klein bottle is assembled from these two tori. (Click image for larger view.)
Assembly of the simplified Klein bottle. (Click picture for animation of the assembly.)