Jitterbug from Sphere to Concave Octahedron?

If the jitterbug were modeled as a sphere collapsing to a concave octahedron, the counterclockwise-rotating triangles would transform from a convex spherical triangle to a flat concave triangle, while the clockwise-rotating triangles would simply invert themselves, exposing the concave surface of the same spherical triangle. This may be difficult to animate in SketchUp.

But that's not what happens. The spheres transform into concave VEs, the concave VEs expand to spheres (or convex VEs), and the concave octahedra simply turn themselves inside out. I'm working on an illustration of this.

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