2. Flat patterns

2.1. Triangular Tiling Pattern. Because Pacioli and da Vinci used only equilateral triangles for the pyramids of the elevations, they could not make elevations of polyhedra with faces other than triangles, squares or pentagons (Figure 10). We can however extend the original concept of elevation to the field of flat tilings with triangular and/or square tiles (Figure 11).
Figure 10: Extension to flat patterns.
Figure 11: Elevated triangular pattern.
Figure 12: Paper model of the elevated triangular pattern.
Figure 13: Demonstrating the strength
To make the flat pattern models we can use the same paper elements as we have used for the polyhedra (Figure 12). The resulting structure turned out to be very stable as is shown by one of the workshop participants (Figure 13). Another thing that was introduced in the workshops was the use of different color patterns (Figure 14).
Figure 14: Introducing color patterns
2.2. Double Weave. In La Divina Proporione [1] the concept of elevation is introduced as an operation applied on polyhedra in one direction only: pyramids are placed on the faces at the outside of the polyhedron. When working on flat patterns we can apply this operation in both directions. When we make pairs of elements as is shown in Figure 15, we can indeed create a structure that can be seen as an elevation in two directions. In Figure 16 we can see the front and the back side of such a double woven elevated pattern.
Figure 15: Double element.
Figure 16: Double woven elevated pattern.