Takahashi found this idea too simple and was stimulated to think of something
topologically more interesting than the Aryan occultism. He came upon the
*periodic minimal surfaces* of H. A. Schwartz and his successors.
For someone living on such a surface there would be many looped paths leading
back home, like tunnels in a termite mound. Modern science fiction echoes the
serious suggestions of John Wheeler and other modern cosmologists of
multiply-connected universes.

The present series of pictures are part of a sustained effort to promote the use of these surfaces in engineering, design and art and to introduce shapes more sophisticated than those of Takahashi’s better-known predecessor in geometrical design, Isamu Noguchi and his contemporary, Shigeru Ban. Ban has produced buildings using paper cylinders, but is constrained to using only developable surfaces (with zero Gaussian curvature). Takahashi seeks to escape from this and is exploring ways of manufacturing sheets of various materials with hyperbolic curvature. As with Buckminster Fuller’s geodesic domes, where the curvature is spherical, the major problem is in joining the sheets elegantly.