4. 3D objects from 2D structures

4.1. The Platonic Solids. The next step is to apply the concept of knot-shaped holes on 3D objects. There are five Platonic solids. Of these, the tetrahedron, the cube and the dodecahedron have in common the fact that at each vertex three faces meet. We can place a trefoil knot on these vertices as in Figure 22.
Figure 22: Knot placed on a vertex of a solid
On each of the faces of the solid we will get a net of connected knots like we had in the planar structures in section 2. And after adding the soap film surfaces we get the double layer objects shown in Figures 23, 24 and 25.
Figure 23: Base: tetrahedron
Figure 24: Base: cube
Figure 25: Base: dodecahedron
4.2. The Archimedean Solids. Also the Archimedean solids can be used as a basic structure for a three- dimensional interwoven single surface object. For the example shown in Figure 26, the snub cube is used as the basic structure. The object is built out of a single continuous surface
Figure 26: Base: snub cube