Cloud Nine (tensegrity sphere)
Cloud Nine is the name Buckminster Fuller gave to his proposed airborne habitats created from giant geodesic spheres, which might be made to levitate by slightly heating the air inside above the ambient temperature.
Geodesic spheres (structures of triangular components arranged to make a sphere) become stronger as they become bigger, due to how they distribute stress over their surfaces. As a sphere gets bigger, the volume it encloses grows much faster than the mass of the enclosing structure itself. Fuller suggested that the mass of a mile-wide geodesic sphere would be negligible compared to the mass of the air trapped within it. He suggested that if the air inside such a sphere were heated even by one degree higher than the ambient temperature of its surroundings, the sphere could become airborne. He calculated that such a balloon could lift a considerable mass, and hence that 'mini-cities' or airborne towns of thousands of people could be built in this way.
A Cloud Nine could be tethered, or free-floating, or maneuverable so that it could migrate in response to climatic and environmental conditions, such as providing emergency shelters.
Eric Vinicoff's novel "Maiden Flight" (Baen Books, ISBN 0-671-69795-1) postulates a post-nuclear holocaust world in which humanity has taken up residence in underground cities known as enclaves, or aerostat cities very similar to the Cloud Nine concept - housing populations in the thousands, approximately a mile or so in diameter, heating the interior atmosphere a few degrees above the outside air temperature to generate lift. By increasing or decreasing the temperature to vary the lift, the cities rise or lower to different wind patterns in order to migrate.