1.3. The Elevated Platonic Solids. To build the models of the Elevated Platonic Solids (Figure 5) we need only three different elements that have to be glued together. Because I was not happy with this solution, which especially at workshops caused a lot of trouble, I decided to develop the element in such a way that glue was no longer needed. This resulted in the element of Figure 6.
Figure 5: Elevations of the Platonic solids.
Figure 6: Element for construction.
This new element, based on the equilateral triangle, can be used to build the models of da Vinci’s tetrahedron, octahedron and icosahedron (Figure 7). Note that I took the liberty to “elevate” not exactly to the height that Pacioli described. But the original construction can be easily recognized (Figure 8)..
Figure 7: Da Vinci – Elevations of tetrahedron, octahedron and icosahedron.
Figure 8: Models of the elevations of tetrahedron, octahedron en icosahedron.
1.4. Variation of the Shape of the Element. Because, with my way of making the models, the height of the elevation was no longer fixed, I decided to experiment a little more with this height as well as with the shape of the connection part of the elements. In Figure 9a a new shape is shown. To build the model of the elevated tetrahedron you still need four elements, but the elevation height is chosen so that he outer shape is a cube. So with four equal parts we have build a cube now (Figure 9b).
Figure 9ab: The new element and the new model of an elevated tetrahedron.