5. Grid transformation

Another, and perhaps even better way to construct real 3D structures based on Leonardo grids appeared to be the use of transformation of the basic Leonardo grid from 2D to 3D. The process can be described as follows: we can start with any pattern in which we can find a hexagonal hole. We now keep the 6 sticks around this hole connected and change the hexagon from flat to skew. This change will cause a transformation of the sticks, which are connected to the first 6 sticks. The six parallelogram shaped holes in the pattern will also be parallelogram shaped at the end of the process. But one of the connections around the triangle holes will get loose. The resulting structure now can be used as a layer with which we can create space frames.
Figure 27: Leonardo grid 2D
Figure 28: Halfway between
Figure 29: Leonardo grid 3D
The discovery of this process lead to many designs of Leonardo grid space frames because the process could be applied on all the flat basic patterns. We can also start with a square hole in a pattern. In the same way the flat hexagon is transformed into a skew hexagon, a flat square can be transformed into a skew square. The over a hunderd different patterns that I had drawn as possible designs for the domes can now be transformed to Leonardo grid space frames. In the illustrations you can see some examples of the resulting space frames.
Figure 30: Space frame grid A
Figure 31: Space frame grid B
Figure 32: Space frame grid C
Figure 33: Space frame grid D
Figure 34: Space frame grid E
Figure 35: Space frame grid F
6. Dynamic space frames

Just as in the double layer structures the Leonardo grid space frames also have dynamic properties.
The sticks can be slid along each other and so the total construction can be pressed together or stretched. To show this we will go back to the skew hexagon first. In Figures 36, 37 and 38 you see three stages of the sliding process. And we can extend that to a complete layer as in Figures 39, 40 and 41. In the total movement it looks as if there is some twist in the structure. The shrinking and growing of the structure is in a way a spiral movement. This can be best viewed in animation.
Figure 36: Sliding first stage
Figure 37: Sliding second stage
Figure 38: Sliding third stage
Figure 39: Sliding first stage
Figure 40: Sliding second stage
Figure 41: Sliding third stage