The Cãlugãreanu, White, Fuller Theorem

1. A doubly-encircled band is topologically equivalent to a band with T=2.
2. At any point on this band, Lk = T + W (T=Twist, W= Writhe; W measures the extent to which coiling of the central curve has relieved local twisting of the cord)
3. The Writhe connects a single band in 2D space with a doubly-encircled band (also in 2D space) via 3D space.
4. Postulate: For T=1, W=1 (Lk =2), the occupancy of 3D space is ~maximum.
5. Postulate: T=1, W=1 and T=1, W=-1 are two distinct solutions (isomers)

1. J. H. White, Am. J. Math., 1969, 91, 693-728; G. Cãlugãreanu, Czech Mathematics J., 1961, 11, 588-625; F. Fuller, Proc. Natl. Acad. Sci., 1971, 68, 815-819.
2. Graphic from: S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, and N. Hatakenaka, Nature, 2002, 417, 397-8. DOI: 10.1038/417397a