Not a problem, we can just shape it like the space covered by rotating the whole thing and make the sofa kind of "bone shaped", then we should be set for 3 dimensions. The only remaining issue would be, where to put the actual sitting area on the bone, but that problem I leave for homework.
3dimensions still allows for more freedom than that though since the couch can stand on end.
I would contend that it's still useful since you'd be able to turn the corner without over-complicating it by getting it into some weird tilt position.
> Not a problem, we can just shape it like the space covered by rotating the whole thing and make the sofa kind of "bone shaped", then we should be set for 3 dimensions.
That might give you a feasible solution, but I doubt it's optimal.