3-sphere two 3-balls. This construction is analogous to a construction of a 2-sphere, performed by gluing the boundaries of a pair of disks. A disk is a 2-ball, and the boundary of a disk is a circle (a 1-sphere). Let a pair of disks be of the same diameter. Superpose them and glue corresponding points on their boundaries. Again one may think of the third dimension as temperature. Likewise, we may inflate the 2-sphere, moving the pair of disks to become the northern and southern hemispheres. After removing a single point from the 2-sphere, what remains is homeomorphic to the Euclidean
Dyson sphere Dyson sphere A Dyson sphere is a hypothetical megastructure that completely encompasses a star and captures a large percentage of its power output. The concept is a thought experiment that attempts to explain how a spacefaring civilization would meet its energy requirements once those requirements exceed what can be generated from the home planet's resources alone. Only a fraction of a star's energy emissions reach the surface of any orbiting planet. Building structures encircling a star would enable a civilization to harvest far more energy. The first contemporary description of the structure was by Olaf Stapledon in his science fiction