I'm not sure which is worse - an onslaught of medical procedures, or being back in Florida before things have cooled off. Good luck with both. Hopefully you're far enough inland at this time of year to not find yourself performing an imitation of Dorothy from the Wizard of Oz.

The inner tube question seems easy enough - an inverted inner tube just looks like an inner tube. It also seems that a similarly inverted sphere would still be a sphere. Even when turned inside-out, the space still closes in on itself.

As I visualize the hyperbolic plane, it seems to be a different kind of inverse (I say this as if that statement makes some sense). It seems to be a more conceptual opposite, in which the space does not curve inward and close in on itself, but curves outward and continually expands. It's a nasty bugger to visualize.

I understand that 2 and 3-dimensional shapes can be "translated" from Euclidian Geometry to Hyperbolic Geometry. I've seen representations of Hyperbolic squares and triangles. I'm trying to imagine if there's such thing as a Hyperbolic sphere, and can only imagine it looking much like the Hyperbolic Plane itself.

As for the moebius strip, I'll have to perform that experiment. I've never worked with moebius strips before. While Algebra and I get along fairly well, I've tended to avoid Geometry like the plague. My College Algebra prof and I battled over it during pre-calc, then I was dragged kicking and screaming into it by Einstein, tied down by Stephen Hawking, and am currently in the process of getting slapped around by Roger Penrose.