Maybe it's hard see, but the thirty strings at the outside form a perfect icosahedron. The icosahedron is one of five platonic forms. The other four are: tetrahedron, cube, octahedron and dodecahedron.
A few basic tensegrities are based on these forms. For example the tensegrity called "icosa" (see well-known) looks like an icosahedron and the tensegrity below looks like a tetrahedron but is in fact a truncated twisted tetrahedron tensegrity.
But the strings in the tensegrity at the right form a perfect icosahedron.
You can turn the structure on the page3D images.
Below, the icosahedron from a different angle. On the right the same picture, with a few black painted strings to make the icosahedron more visible.
The icosahedron below is exactly the same as above. But now the struts are kept in the outside range within the icosahedron instead of reaching to the center of the structure.
The icosahedron at the left is exactly the same as all the others above, only the struts seem to be in strange formation. In fact I combined both variations that are shown above.
Another version, a little larger.
And one more.