Figure 1: Platonic Tensegrity. Two views. Stainless steel. 94x94x94 cm. 2023
Figure 2. Ten Tetrahedra in Tensegrity II, stainless steel, 100x100x100 cm, 2022
Figure 3. Ten Tetrahedra in Tensegrity I, brass, 40x40x40 cm, 2018
The Compound of Five Tetrahedra The compound of five tetrahedra has long fascinated me. In figure 6 below, I show it cast in bronze.
In figure 3 above, there are five tetrahedra,, made of brass tubes which are suspended from one another by wires, and which have a right-handed orientation. The wires themselves form another five tetrahedra which have a left-handed orientation. They are the mirror image of the first five. altogether these are the ten tetrahedra that can be inscribed in a dodecahedron. The wires pass through slots in the tubes without touching, thereby making it a true tensegrity figure.
Figure 2 above is similar to figure 3, but larger and made with stainless steel, instead of brass. Also, the joints are fastened with screws instead of glue, and wire tension is achieved with screws instead of twisting of wires. So, the whole sculpture can be disassembled for transport. Thanks to careful mathematical calculations, I was able to precision machine this piece entirely in stainless steel, allowing it to maintain its beauty in an outdoor setting.
Figure 1 above consist of the same 5 tetrahedra in stainless steel. It is also a tensegrity figure, but with tensioned wires passing closer to the center, creating thereby an icosahedron, suspended in the center. The icosahedron is the intersection of the 5 tetrahedra.
Figure 4. Cube Inscribed on Extended Faces of Dodecahedron, stainless steel and copper, 76x71x71 cm, 2017
Figure 5. Cube Inscribed on Extended Faces of Dodecahedron, brass and aluminum, 45x45x45 cm, 2016
Inscribing a Cub on the Faces of a Dodecahedron
As is very well known, one can inscribe a cube on a dodecahedron with each of its 12 edges on one of the 12 faces of the dodecahedron. Euclid used this to prove the existence of the regular dodecahedron. Not so well known (In fact I have not seen elsewhere except in my own work) is that there is exactly one other way to inscribe the cube on the dodecahedron with one edge on each face, providing that one allows the dodecahedron faces to be extended. This is shown in figures 4 and 5 above.
Figure 6. Compound of five Tetrahedra, cast bronze, 36x36x36 cm, 2018
Figure 7. Coordinate Planes, bronze sheet, 28x28x28 cm, 2018