As shown by cosmologists space is presumably a flat expanse. In his book the Fabric of the Cosmos, Brian Greene shows that one of the possible shapes of this flat universe is a Torus. My question is, are there other shapes that would fulfill the same criteria, if so, how?
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There is quite a nice description of this area in the Wikipedia article on the shape of the universe. As well as the torus possible shapes include the Poincaré dodecahedral space and the Picard horn.
Googling will find you lots of stuff about the duodecahedral shape, and despite its potential for causing sniggers there is quite a bit on Picard's horn as well.
John Rennie
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