Department of Engineering

## Tensegrity Structures with Point Group Symmetry Ih and Site Symmetry Cs

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, Ih , with site symmetry, Cs .

The point groups, Ih 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, Cs , will have a plane of reflection.

### Tensegrity Structure Ih : Cs1

If we choose to have:
1) site symmetry, Cs : σa ;
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 : Cs1 with an orbit of 60 nodes.

### Tensegrity Structure Ih : Cs2

If we choose to have:
1) site symmetry, Cs : σg ;
2) a strut connecting node E to node σc 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 : Cs2 with an orbit of 60 nodes.

### Tensegrity Structure Ih : Cs3

If we choose to have:
1) site symmetry, Cs : σc ;
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 : Cs3 with an orbit of 60 nodes.