Why do some books talk about universe as a torus, a saddle etc? The universe cannot be defined without physical things like matter, right? The edge of the universe is measured from one furthest matter to the other, right? The universe can take any shape. The shape of the universe is formed due to the interaction between matters via forces, like gravitational force. If the universe is a sphere, it only means that the gravitational force among all the matters are in such a way that, it happens to form a sphere. Our universe's shape can change with time. Right?