Rotations Per Minute Needed to Balance a Top

I have little to no experience with this area of physics, so don't assume I know certain things. A cone is spun (with the tip down) at a constant, not decreasing, RPM (Rotations per Minute). What is the minimum RPM for it to stay there without falling, and (if possible) the minimum RPM necessary to make it seem as thought it might be stationary? If dimensions are needed, I would not be able to give them, but I can give ratios, or I can put it in units that have no real world value.