It's interesting, isn't it, how it seems to be impossible to make a
stable levitating platform just using magnets.

I keep trying to visualise various arrangements of magnetic poles which
ought to work, but of course have never succeeded.

I've owned two or three levitating toys in the past, but all of them
rely on a closed loop electromagnetic control system, rather than
passive magnets. Perhaps the most impressive was the one which relied
on the object spinning really fast like a top to produce gyroscopic
forces - it hovered higher than any of the others and didn't require
anything above it, so it really did seem to be in mid-air.

More recently I bought one which doesn't require the object to spin,
but the hovering height isn't very impressive.

The only hovering effect from passive magnetic fields I've seen is due
to the paramagnetic effect. You arrange an array of magnetic cubes in
a certain way, and then hover a tiny piece of diamagnetic material over
it. Again, though, the hovering distance is very small, and it
certainly wouldn't support a settee!

SteveT