When we tiled our lounge, kitchen and dining rooms recently, there was a lot of cutting to do around the fiddly corners, and a lot of waste, too. That got me thinking: with the right precise measurements, you could "print" exactly the right tiles for a space, custom-made to fit perfectly. Or maybe you could use a robot that trundles around the room extruding and baking ceramics in specified shapes in-place. Either way, it should be possible to fit tiles perfectly to a floor with zero waste. The only question is whether it would be more economical that way.
Mokalus of Borg
PS - I guess it depends how much more expensive custom-shaped tiles are.
PPS - And whether you accidentally break any.