7. More Layers

7.1. Three-layer Structures. By applying connected knots we were able to create double layer structures. Knots are related to star polygons. The fivefold knot is derived directly from the five pointed star, a pentagon of order 2. With bigger polygons, like for example the octagon, higher orders also occur. The structure shown in Figure 42 is made by applying the star octagon which has order three. The result is a three-layer interwoven structure built with one continuous surface. There is a nice way to create three- layer structures in 3D: we can use the interwoven layer structure of Figure 43, which has three separate layers, as ‘material’ to make a folding pattern for an icosahedron. The result will be the three-layered single surface object shown in Figure 44.
Figure 42: 3 layers - 1 surface
Figure 43: 3 layers - 3 surfaces
Figure 44: 3 layers - 1 continuous surface

References

[1] M.C. Escher, Grafiek en Tekeningen, Uitgeverij Tijl, Zwolle, 1960.
(The Graphic Work of M.C. Escher, Meredith Press, New York, 1960; Ballantine Books, 1971; Wings Books, New York, 1996.)
[2] Doris Schattschneider, M.C. Escher: Visions of Symmetry, Abrams 2004