Six stages in a Jitterbug transformation, attributed to Buckminster Fuller. Clockwise from the bottom as it appears on opening, there is a cubotahedron, a regular icosahedron, an alternate irregular icosahedron, an octahedron, an irregular icosahedron, and an alternate icosahedron. This is an exploration of six arrays based on these six indicated polyhedra that appear to be stages in the same kind of transformation of whole arrays.

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The link below is to an animation of what is decribed above, in more stages.

Corresponding to the cycle shown above, this is a Cuboctahedron-Octahedron array.

This shows an array of Icosahedra and irregular Icosahedra. Note that edges that would constrain rotation of triangles are left out, and only the triangles that rotate are paneled.

Here is shown an irregular Icosahedron-Icosahedron array, where the positions in the array are reversed.

This is the Octahedron-Cuboctahedron array, corresponding with the octahedron at the top of the cycle.

Continuing, this is the other irregular Icosahedron-Icosahedron array.

And last, the alternate Icosahedron-irregular Icosahedron array, leading back to the Cuboctahedron-Octahedron array.

This multi-jitterbug effect in continuous motion through all the stages has yet to be verified, either in a physical model, or virtually. The link below is to an animation that is convincing, if not definitive.