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
Bernal sphere optimum mass-efficiency at providing radiation shielding. O'Neill envisioned the next generation of space habitat as a larger version of "Island One". "Island Two" would be approximately 1800 meters in diameter, yielding an equatorial circumference of nearly six and a half kilometers (four miles). The size was driven by economics; the habitat was to be small enough to allow for efficient transportation within the habitat and large enough to support an efficient industrial base. Bernal sphere A Bernal sphere is a type of space habitat intended as a long-term home for permanent residents, first proposed in 1929 by John Desmond Bernal.