• There are three possibilities for the curvature of the universe: space can be flat, spherical or hyperbolic
• The geometry of the universe depends on its curvature and also on its topology, which governs the way space is connected and so determines if it is finite or infinite
• Measurements of the cosmic microwave background constrain the curvature of the universe and provide hints about its topology
• Recent data suggest that the universe might be multiply connected, like the left- and right-hand sides of the screen in a computer game
• Since the early 1990s the number of cosmo-topologists around the world has grown to more than 50

For centuries the size and shape of space has intrigued the human race. The Greek philosophers Plato and Aristotle claimed that the universe was finite with a clear boundary. Democritus and Epicurus, on the other hand, thought that we lived in an infinite universe filled with atoms and vacuum. Today, 2500 years later, cosmologists and particle physicists can finally address these fundamental issues with some certainty.
Surprisingly, the latest astronomical data suggest that the correct answer could be a compromise between these two ancient viewpoints: the universe is finite and expanding but it does not have an edge or boundary. In particular, accurate maps of the cosmic microwave background - the radiation left over from the Big Bang - suggest that we live in a finite universe that is shaped like a football or dodecahedron, and which resembles a video game in certain respects.