Inversion of the cube and related forms: configuring discourse otherwise?

Time for Provocative Mnemonic Aids to Systemic Connectivity? (Part #4)

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Paul Schatz was seemingly frustrated by the conclusion of the above approach. It did however lead to a much more fruitful exercise with respect to inverting or everting the cube for which he is widely known, as illustrated by a number of videos (Charles Gunn, Schatz Cube Eversion, Vimeo, 25 April 2017; Daniel Wall, The Schatz Cube, or inverting cube, YouTube, 8 October 2010; Ryser Andreas, Invertible Cube, 30 March 2013; Invertible cube; Dolf Perenti, Inverting Cube, YouTube, 13 July 2011). Flexible card models are also marketed with commentaries (model; model) as with many wireframe models known as Hexyflex.

This approach is described by the Paul Schatz Foundation in the following terms:

On 29 November 1929, Paul Schatz set in motion the cube, the solid until then representative of everything that was earthbound, rigid -- static, even. In the course of his studies of the pentagonal dodecahedron, that to some degree most noble of the Platonic solids, he discovered that the cube can initially be subdivided into two stellated solids and one cube belt. It is the cube belt liberated from its interlocking parts that illustrates so impressively the dynamic qualities inherent in the cube. The model turns the richly varied movements of the cube into a tactile experience. Moreover, the pulsating movement inspired Paul Schatz to build several machines, of which the most famous are the Turbula, the Inversina and the Oloid.

The potential of this approach is consistent with that widely framed in terms of the need for "thinking outside the box". Reference to "inside the box" is considered analogous with the current, and often unnoticed, assumptions about a situation. The associated dynamics are consistent with arguments for fluidity in creative thinking (Douglas Hofstadter, Fluid Concepts and Creative Analogies: computer models of the fundamental mechanisms of thought, 1995). There is a case for recognizing the analogy implied by literal use of "the box" as a widely employed method of punitive solitary confinement, as vividly described by Shruti Ravindran (Twilight in the Box: what does solitary confinement do to the brain? Aeon, 27 February 2014). Widespread conventional dependence on a cuboid framework may well constitute an analogous form of a solitary confinement.

Other polyhedral inversions and mapping applications? The inversion movement recalls that which fascinated Buckminster Fuller with respect to the cuboctahedron of 12 vertices (H. F. Verheyen, The complete set of Jitterbug transformers and the analysis of their motion, Computers and Mathematics with Applications, 17, 1989). Many videos of that "jitterbug" movement exist (Buckminster Fuller's Jitterbug, YouTube, 5 May 2007; Joe Clinton, R. Buckminster Fuller's Jitterbug: its fascination and some challenges, YouTube, 15 March 2008; Bucky's "Jitterbug" -- Vector Equilibrium, 16 October 2008).

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