Tensegrity Structures with Point Group Symmetry I_{h} and Site Symmetry C_{s}

At the simplest level, a tensegrity structure can be made with one orbit of cables and one orbit of struts. Our aim is to show how the local site
symmetry can be used to solve the equilibrium of nodal configurations of such simple tensegrity structures. Here, we consider the point group symmetry, I_{h} , with site symmetry, C_{s} .

The point groups, I_{h} have 5-fold axes of symmetry.
These symmetry groups contain twelve 5-fold, twenty 3-fold, and
fifteen 2-fold axes and has 120 symmetry operations. They are related to the symmetry of the
icosahedron. The site symmetry, C_{s} , will have a plane of reflection.

Tensegrity Structure I_{h} : C_{s1}

If we choose to have:
1) site symmetry, C_{s} : σ_{a} ;
2) a strut connecting node E to node C_{ 2a} with tension coefficient t_{ s} ; and
3) a cable connecting nodes E to node C^{ + }_{51}, and node C^{ - }_{51} with tension coefficient t_{ t} ,
then solution t_{ t} / t_{ s}= - 2.62 gives the tensegrity structure I_{ h} : C_{s1} with an orbit of 60 nodes.

Tensegrity Structure I_{h} : C_{s2}

If we choose to have:
1) site symmetry, C_{s} : σ_{g} ;
2) a strut connecting node E to node σ_{c} with tension coefficient t_{ s}; and
3) a cable connecting nodes E to node C^{+}_{51}, and node C^{-}_{51} with tension coefficient t_{ t} ,
then solution t_{ t} / t_{ s} = - 1.81 gives the tensegrity structure I_{ h} : C_{s2} with an orbit of 60 nodes.

Tensegrity Structure I_{h} : C_{s3}

If we choose to have:
1) site symmetry, C_{s} : σ_{c} ;
2) a strut connecting node E to node C_{ 2d} with tension coefficient t_{ s} ; and
3) a cable connecting nodes E to node C^{ + }_{51}, and node C^{ - }_{51} with tension coefficient t_{ t} ,
then solution t_{ t} / t_{ s} = - 3.93 gives the tensegrity structure I_{ h} : C_{s3} with an orbit of 60 nodes.