Department of Engineering

## Tensegrity Structures with Point Group Symmetry T

Tensegrity structures with point group symmetry, T , will have the symmetries of rotations, but not reflections, of a tetrahedron. Since this T group tensegrity structure originates from tetrahedron, this structure has 7 symmetry axes, which are along the vertices and vertex diagonals of tetrahedron. The twelve symmetry operations; the identity, E, rotations by 120° and 240° about the vertices, 1, 2, 3 and 4; { C31, C32, C33, C34, C231, C232, C233, C234 }, and rotation by 180° about the a, b, and c axes, { C2a, C2b, C2c }, form the symmetry group of the example structure. These twelve symmetry operations constitute the symmetry group T. We assume one regular orbit of nodes: there are 12 nodes, which have one to one correspondence with the 12 symmetry operations.

### Tensegrity Structure T1

If we choose to have:
1) a strut connecting node E to node C2a with tension coefficient ts;
2) cable 1 connecting nodes E to node C31, and node C231 with tension coefficient tt; and
3) cable 2 connecting nodes E to node C32, and node C232 with tension coefficient td;
then solution tt/ts = td/ts = -1 gives the tensegrity structure T1.

### Tensegrity Structure T2

If we choose to have:
1) a strut connecting node E to node C2a with tension coefficient ts;
2) cable 1 connecting nodes E to node C31, and node C231 with tension coefficient tt; and
3) connecting nodes E to node C33, and node C233 with tension coefficient td;
then solution tt/ts = td/ts = -0.67 gives the tensegrity structure T2.

### Tensegrity Structure T3

If we choose to have:
1) a strut connecting node E to node C2a with tension coefficient ts;
2) cable 1 connecting nodes E to node C31, and node C231 with tension coefficient tt; and
3) cable 2 connecting node E to node C2b with tension coefficient td,
then solution tt/ts = td/ts = -1.74 gives the tensegrity structure T3.

### Tensegrity Structure T4

If we choose to have:
1) a strut connecting nodes E to node C31, and node C231 with tension coefficient ts;
2) cable 1 connecting nodes E to node C32, and node C232 with tension coefficient tt; and
3) cable 2 connecting nodes E to node C33, and node C233 with tension coefficient td;
then solution tt/ts = td/ts = -1.5 gives the tensegrity structure T4.

### Tensegrity Structure T5

If we choose to have:
1) a strut connecting nodes E to node C31, and node C231 with tension coefficient ts;
2) cable 1 connecting nodes E to node C32, and node C232 with tension coefficient tt; and
3) cable 2 connecting node E to node C2a with tension coefficient td,
then solution tt/ts = td/ts = -3 gives the tensegrity structure T5.

### Tensegrity Structure T6

If we choose to have:
1) a strut connecting nodes E to node C31, and node C231 with tension coefficient ts;
2) cable 1 connecting nodes E to node C32, and node C232 with tension coefficient tt; and
3) cable 2 connecting node E to node C2b with tension coefficient td,
then solution tt/ts = td/ts = -2.47 gives the tensegrity structure T6.