...in the toroidal universe, the lasers will remain parallel, but will wrap around the 2d donut and smack you up the back of the head! But the 2d geometry is still Euclidean or 'flat'.

I don't know how it works for the soccer ball... Bend It Like Beckham?

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If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it... of the manifestations of the profoundest reason and the most radiant beauty, which are only accessible to our reason in their most elementary forms...
Albert Einstein