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I know what you mean - the first time you take a "print in place" functional model off a 3D printer it's kind of mind blowing! Really opens your eyes to the possibilities of this technology.

Regarding the hard edges: there's no one-click kind of way to do what you're asking, but there's certainly no reason you can't import the model in one of the many 3D modelling tools out there and apply a chamfer or fillet to the edges to achieve your desired result. You would need to be cautious about removing too much material around the areas where the hinges are held in place though, as it would be easy to weaken those areas enough to cause the hinges to break free of the cubes.

Happy fidgeting!