8. Weave Grids 3D

8.1. Black/White - Left/Right. In his article “Weaving, Mother of Tensegrity” [5] Kenneth Snelson writes, and he illustrates it with a picture that is similar to Fig 42a: “Each woven interaction produces its rotational complement. Just as the individual crossings of filaments have their helical axes so each square in a plain weave has its opposite. Each cell’s neighbours are its mirror form like alternate squares on a chess board.” And this is exactly what is happening in the helical hole surfaces: neighbouring holes are each other’s mirror images. If one spiral hole is clockwise, his neighbour hole is counter clockwise. When we make this relation visible like in Figure 42d and 42e we can apply the soap film method again to create the surface shown in Figure 42f.
Figure 42a: Snelson
Figure 42b: Left/Right
Figure 42c: Black/White
Figure 42d: One hole
Figure 42e: First twist
Figure 42f: Helix
8.2. Black/White Tiling on Helical Hole Surfaces. One of the important discoveries Kenneth Snelson talks about in his article is 3D weaving. The examples he shows are based on space frames. Also helical hole surfaces can be used to generate 3D weaves. And this method is in a way exactly the same as the generation of the weaves from the checkerboard colored tilings that we have discussed in Sections 2 and 3: as you can see in Figure 42g the helical hole surface can be covered with a black/white tiling by projecting the underlying coloring on it. And this tiling can be transformed into a weaving again. It all looks the same but there is one big difference: the weaving that we have created now is a 3D weaving. Each thread in the weaving is connected with threads at two different levels.
Figure 42g: Projecting
Figure 42h: Tiling
Figure 42i: Weaving
8.3. 3D Weaves. To make this more visible I have made two examples of these 3D weaves. The first one is based on the Archimedean tiling (4.4.4.4) and the second one is based on the tiling (3.6.3.6).
Figure 43: 3D weave square
Figure 44: 3D weave hexagonal