This double-layer sphere has the tendon network of a tensegrity icosahedron as its inner layer (green) and an asymmetric version of the same network as its outer layer (pink). (This is the same tendon topology which the jitterbug has.)

The interlayer tendons (white) which connect the two layers connect the geometrically corresponding points to each other. It's as if the interlayer tendons traced the path by which the vertices of the inner tensegrity octahedron were expanded to get to the outer one. Such interlayer connectivity is only possible at this lowest frequency. At higher frequencies, tendons connected in this way interfere with the struts.

You can read more about this structure at my page Laminar 2v Tensegrity Octahedron.

Both this variation and the original "2v Octa Sphere" appear in the Java3D-Based Tensegrity Viewer. Only the original appears in the Java-Based Tensegrity Viewer since the difference between the two structures isn't apparent without the interlayer tendons whose display is omitted in the Java-Based Tensegrity Viewer.