Visualization of memorable complex configurations

Oppositional Logic as Comprehensible Key to Sustainable Democracy (Part #4)

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A verbal argument, especially when dependent on mathematical and logical jargon, needs to be presented otherwise if degrees of coherence are to be apparent to many -- hence the many polyhedral depictions in the forum on Oppositional Geometry. To the extent that politics achieves a degree of credibility by appealing to symbols of coherence, most notably the sphere, there is a case for positioning points, principles, and lines of argument in some form of spherical configuration. Of particular interest is the manner in which the simplest polyhedra, widely known from architecture, can be employed to map strategic concerns -- especially in the case of those polyhedra which are the closest approximations to a sphere.

It is in this sense that the use made by oppositional geometry (logic) of variants of the octahedron is of particular interest -- notably as being the dual of the ubiquitous cube. Whilst the cube has long been used to illustrate simpler logical relations, it is the truncated octahedron that has become a particular focus in its dual form, namely the tetrahexahedron (as discussed separately and by Alessio Moretti, The Geometry of Logical Opposition, 2009).

There appears to be a complex of insights potentially associated with geometrical transformations of the octahedron, including the stellated octahedron (Framing Global Transformation through the Polyhedral Merkabah: neglected implicit cognitive cycles in viable complex systems, 2017).

Variety of polyhedral arrays
8-fold cubic array	12-fold icosahedral array	12-fold cuboctahedral array	14-fold tetrahexahedral array
Prepared with features of the Stella Polyhedron Navigator software package

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