Recall the Cuboctahedron, which Fuller calls the "Vector Equilibrium" (VE).
The VE 
With a Cuboctahedron (VE) constructed out of sticks and rubber vertices, Fuller often demonstrated what he called the "Jitterbug" motion. The Jitterbug shows how the VE can fold up into an Octahedron as well as how an Octahedron can expand in the VE.
VE position 
Jitterbug in motion

Octahedron position 
The Jitterbug has 8 triangular faces. As these 8 faces rotate, they also move radially inward or outward from the center of volume along its 4 rotation axes.
Motion along 4 rotation axes

These are the same 4 rotation axes that we used to rotate the 4 cubes.
Jitterbug rotation axes 
Fuller pointed out that between the VE and the Octahedron positions, the Jitterbug will pass through an Icosahedron position.
Jitterbug defines the Icosahedron

If we allow the 8 rotating triangles to interpenetrate each other, then the Jitterbug can rotate and contract into two intersecting tetrahedra to define a cube.
Jitterbug in Octahedron position 
Jitterbug in motion

Jitterbug in Cube position 
Further rotation and contraction results in the definition of another Icosahedron.
Jitterbug in Cube position 
Jitterbug defines the Icosahedron

Jitterbug in Icosahedron position 
When the 120 Polyhedron is considered with all of its defining, internal polyhedra, many Jitterbugs can easily be identified. These Jitterbugs are not all in the same open position, nor of the same scale. Here is an illustration looking into the array of polyhedra through a regular Dodecahedron vertex. (The outer edges of the 120 Polyhedron are not shown.)
Looking into a Dodecahedron vertex 
In the next sequence of illustrations, I display various Jitterbugs by changing the associated polyhedron into a solid appearance. All of these Jitterbugs have the same face centered rotation axis passing through the regular Dodecahedron's vertex.
A Jitterbug in the Icosahedron position 
A Jitterbug defined by Cube edges 
A Jitterbug in the Octahedron position 
A Jitterbug in the VE position 
A Jitterbug in the Tetrahedron position 
It is difficult to see the Jitterbug defined by the Cube's edges in the above illustration, so here is a different perspective. The Dodecahedron is shown with the 5 Cubes. Some of the edges of the Cubes are outlined in black. Filling in the triangular faces in black reveals the Jitterbug.
A Jitterbug defined by the Cube edges 
Notice the variation in the triangular face sizes and orientations. These variations show that there are many different Jitterbugs operating within the 120 Polyhedron.
The Octahedron is one position which the Jitterbug passes through. There are 5 Octahedra in the 120 Polyhedron. Here is a movie showing the dynamics of 5 Jitterbugs. Note that the Jitterbugs define both the Icosahedron and the Dodecahedron.
Five Jitterbugs passing through and
defining an Icosahedron and Dodecahedron 
Here are some additional combinations of polyhedra which I find particularly interesting.
Ten Tetrahedra 
Five Octahedra 
Five Octahedra 
Five Rhombic Dodecahedra 
5 Octahedra, Icosahedron, Dodecahedron 
Surface waves over the 120 Polyhedron 