Images: Dubai's skyscraper in motion

The circular core of the tower would remain stationary, and the rest of the structure would rotate around it. "Everything starts from the core," Fisher said. "The core is the only structural element of the building. Somehow it takes us to nature. It's like the trunk of a tree."

This tentative floor plan for the Dubai tower gives a sense of how a villa could be laid out, with residents able to do a good deal of customizing. "You have a cinema, you have a spa, whatever you can desire," Fisher said. (The Moscow floor plan is more purely triangular, with slightly convex sides.)

Despite the movement of the floors, the building will have a "normal plumbing system," he said. To get water into or out of the residence, a pipe from the villa would connect to a pipe in the core much as a bomber or fighter jet links up with an aerial tanker for midair refueling.