Spherical representation consistent with sense of globality

Embodying Global Hegemony through a Sustaining Pattern of Discourse (Part #5)

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Whilst the argument can be most readily presented in tabular form, this is necessarily in fundamental contrast with any global sense that might be enabled by a spherical representation. The case for this can be variously argued (Spherical Configuration of Categories -- to reflect systemic patterns of environmental checks and balances, 1994; Spherical Accounting: using geometry to embody developmental integrity, 2004; Engaging with Globality through Cognitive Crowns, 2009; Adhering to God's Plan in a Global Society, 2014). It is also the case that some consideration was originally given in the Human Values Project to the spherical configuration of value polarities.

Insights suggested by spherically symmetrical polyhedra: With respect to the table as a whole, it is intruiging to consider the implications of the suggested column sequence being mirrored in some way with the row configuration.

	Tetrahedron	Cube Octahedron	Icosahedron /Dodecahedron	Archimedean polyhedra
Tetrahedron
Cube Octahedron
Icosahedron Dodecahedron
Archimedean polyhedra

The possibility acquires greater interest through relating value polarity to the duality of projective spherical geometry. This is the manner in which a given polyhedron is transformed into its dual -- with an apex becoming the centre of a face, and a face becoming an apex. The above table might then be presented such as to distinguish columns and rows in those terms. *** points/lines

	Tetrahedron	Cube	Icosahedron	Archimedean polyhedra
Tetrahedron
Octahedron
Dodecahedron
Archimedean polyhedra ****

Of particular inerest is the fact that the tetrahedron is its own dual.

Animation of morphing between Platonic polyhedra and their duals (all animations prepared using Stella Polyhedron Navigator)
Variants of Tetrahedron-to-Tetrahedron morphing potentially indicative of a "tetrahedral conversation" and the challenge to it?
Variants of Cube-to-Octahedron morphing potentially indicative of a "cubic conversation" and the challenge to it?
Variants of Icosahedron-to-Dodecahedron morphing potentially indicative of a "dodecahedral conversation" and the challenge to it?

The potential significance of morphing between duals was highlighted in animations in previous exercise in the case of both the G-20 major economies and of the G20 developing nations (Global strategic significance of 20-fold configurations, 2015). Each may be mapped onto a dodecahedron morphing into an icosahedron raising valuable questions as to the discourse connectivity in either or both modalities. The animation for the developing country group is reproduced below.

As indicated previously, this may also be explored in terms of polyhedral representation (Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization, 2008; Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors, 2008). The latter presents a mapping of the G20 Group onto an icosahedron then complexified to an icosidodecahedron and a rhombicosidodecahedron.

G20 Group of Developing Countries (3 countries which are also part of the G20 Group of Major Economies have been excluded for the purposes of this representation)
Mapped onto 20 vertices of a dodecahedron	Mapped onto 20 faces of an icosahedron

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