Any interesting thoughts? a cube have 6 sides and 8 corners, you cannot make one cube fit into another. But a square has 4 sides and 4 corners, therefore you can make one fit into another. An n-dimensional object has got lesser corners than sides, therefore you can make no n-dimensional object fit into another perfectly, when n>2. (a + b)2 = a2 + b2 + 2ab a b ------|----- Inside the square, there is another square, c2. it cuts between a and b on all 4 sides. What's left is 2ab so a2 + b2 = c2 An n-dimensional object inside another cannot cut all sides into whole numbers since it cannot cut all sides at all for n>2.