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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
s2 = (d-l)2 + d2 + l2
In the particular case S = square root of 3/2 l  the two extremes coincide, and  d=1/2 l.

MODEL DESCRIBING THE RELATIONSHIP TO A STABLE CONSTRUCTION ALTHOUGH WITH INFINITESIMAL MOBILITY.

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.

TENSEGRITY ICOSAHEDRON