Wednesday, March 17, 2021

The NbO net and 3D weaving

In "Three-periodic nets and tilings: regular and quasiregular nets," Friedrichs, O'Keefe, and Yaghi dub the net of straight lines found in the D-surface 'nbo' after the chemical bond structure in niobium monoxide, NbO (shown above.) The same net is discussed in Peter Pearce's "Structure in Nature is a Strategy for Design,"
and in A. H. Schoen's "Infinite periodic minimal surfaces without intersections",
but without either obtaining a name for it.
From its similarity to the square grid on the plane-- both consist of straight lines meeting at 90-degree angles-- I expect that the nbo net and its underlying Schwarz D-surface will be important in the future of 3D weaving. Of course, there is another famous 3D grid that is composed of straight lines meeting at 90 degrees: what is special about nbo is that the lines meet only two at a time as in normal weaving.

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