Department of Engineering

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.