Icosahedral Tensegrity by Tensioning Cables

This activity belongs to the GeoGebra book GeoGebra Principia. One of the pioneers of tensegrities, Buckminster Fuller, showed particular interest in this type of tensegrity. It consists of a structure formed by three pairs of parallel bars, perpendicular to each other, tensioned by cables. The whole structure constitutes a non-convex icosahedron, known as the Jessen's icosahedron , whose vertices do not occupy the same positions as in a regular icosahedron. We start with bars attached in pairs. When tensioned, the bars separate until the direction of the resulting force aligns with that of the bar. The ratio between the length of each bar and each cable will then be exactly (≈1.63). Note that in a regular icosahedron, this ratio is the golden ratio (≈1.62). We can observe that the angle of the faces of Jessen Icosahedron is 90º.
Author of the construction of GeoGebra: Rafael Losada.

Information: Icosahedral Tensegrity by Tensioning Cables