The number of facets required to be "smooth" changes based upon how large the object is.
There is no single "magic" number of facets that will work in all sizes.
https://stonysmith.com/wired/scaling.asp
If you are designing a 1mm diameter object, then even 16 sides will appear round-ish.
But if you're designing a 50mm circle, you will need to be up in the thousands.
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Math Alert:
The technical answer is: pick the material you want to print in, then look at the design rules page.
You will find there a number for "Minimum Detail" size.
The smoothest
possible face dimension will be one half of that size.
Example: WSF has a minimum detail of 0.2mm
Therefore you need faces of at most 0.1mm width.
For a 10mm circle, the circumference is 62.8mm so you need ~650 sides.
Note: as your objects get larger, this presents a bit of a problem because each "face" has to be a triangle, and Shapeways has a one million triangle limit per model. That means reducing the number of faces and/or getting crafty with how the model is designed.