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stability and motion in 3D

**The thoracic chain model in 3D - is a stable tensegrity icosahedron, describing the relationship between structure and function**

The following is a mathematical model related to the tensegrity icosahedron explaining why it is a stable construction and still maintain an infinitesimal mobility. Since the tensegrity icosahedron represents an extremal point of the below relation, it has infinitesimal mobility: a small change in the length by stretching the tendons results in a much larger change of the distance of the struts.

**Defenition of the 3D chain model**

s = distance connecting tension elements, yellow = 1.732

d = side length of a cube green = 1

*l* = length of struth, compression elements, blue = 2

s^{2} = (d-*l*)^{2} + d^{2} + *l*^{2}

In the particular case S = square root of 3/2 l the two extremes coincide, and d=1/2 l.

Different shapes of tensegrity icosahedra, depending on the ratio between the lengths of the tendons and the struts. The thoracic chain model shows the relation square root of 3/2 to 1/2.