Since the Möbius band is such a cool object, it follows that anything made from a Möbius band or in the shape of a Möbius band is therefore also supercool. Also: the bigger, the better. So how about a Möbius house?
Korean architects Planning Korea have come up with a scale model and computer generated images of an amazing house based on the one-sided wonder, which uses the face of the Möbius strip as the roof and walls, with the front and back of the house covered in glass windows. It would take twice as long to paint the outside of your house (it’s also the inside), but otherwise you’d be sitting pretty. I do hope that’s a Möbius shed visible in the background, and a probability tree in the garden.
If you’re looking for something to sit on in your non-orientable domicile – presumably, while wearing your Conjoined Möbius Hat – there’s always this chair, which was incorrectly identified as being a Möbius strip by NotCot, and features a distinctly Möbiusy-looking wooden frame with coloured hanging net, to throw yourself into at the end of a long day of one-sided arguments and twisted stripping (don’t ask).