Vertical arrays of polyhedra implying higher degrees of order

Cognitive Embodiment of Patterns of Governance of Higher Order (Part #6)

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There is no lack of references implying the possibility of "higher" degrees of insight -- whether or not the metaphor is to be challenged. The recognition is obvious in the sequence of academic degrees and qualifications, and related assumptions of IQ. It features in secret societies, as with the degrees of Freemasonry; it is a characteristic of initiations and the associated rituals (Varieties of Rebirth: distinguishing ways of being born again, 2004).

Far less evident is the application of this insight to governance, although wisdom in governance may be readily acknowledged, as with the occasional appointment of advisory bodies (Committee of Wise Persons of the Council of Europe; Committee of Wise Men on the Regulation of European Securities Markets), and solicitation of the wisdom of others deemed especially wise (The Elders). It is indeed unclear how many levels of skill in governance can be usefully distinguished, however these may culminate in the "wise governance" for which strategic sustainability presumably calls.

Arguably a degree of recognition of these distinctions is indicated by the traditional symbolic role of the sceptre (Embodying the essence of governance in ritual dynamics with mace, sceptre, fasces or vajra? 2021; Integrative "orbital" implications: Crown and Sceptre / Sahasrara and Axis Mundi, 2020).

Far more evident is the recourse to arrays of symbolic "pillars" in the articulation of strategies by intergovernmental institutions (Fundamental values and strategic pillars, 2008; Holders of value configurations -- and their "pillars", 2008; Coherent Value Frameworks: Pillar-ization, Polarization and Polyhedral frames of reference, 2008). For example, the European Union has developed various sets of "pillars" that might be understood as the implicit value architecture of a number of strategic initiatives. The EEC was renamed the European Community (EC) upon becoming integrated into the first pillar of the newly formed European Union in 1993. Classic examples include: the Pillars of Ashoka, the Five Pillars of Islam, and the Pillars of Hercules. Less evident however is attribution of distinct levels of significance by inscription at different heights of the pillar.

As an exercise, the following animations are formed by stacking polyhedra selected for the number of vertices associated with each -- rising from 4 at the base to 64 at the top, passing through 8, 16 and 32. These are the numbers which are so fundamental to the binary coding systems of computers -- based on 2ⁿ, where n ranges from 2 to 5. A distinct set of examples could be offered based on the number of edges, or the number of faces.

The numerical attributes of each polyhedra in a stack are presented below as an indication of how it might be used to map qualitative attributes values, concepts or strategies, for example.

Stack A alternative renderings			Stack B alternative renderings
Non-transparent	Rainbow lighting	Transparent	Non-transparent	Rainbow lighting	Transparent

There is an obvious case for including the truncated icosahedron in such a stack. As the stitching pattern for the standard association football, known world wide, it must necessarily be of a fundamental significance as yet to be fully appreciated, as discussed separately (Game ball design as holding insight of relevance to global governance? 2020). It is especially intriguing in that it is a 32-fold pattern which is so familiar, being much more complex than the 8-fold and 16-fold patterns preceding it in the stack. Potentially more intriguing is the pattern of 64 vertices in the polyhedron which follows it -- being so complex that it can only be represented as the 3D projection of a structure in 4D.

The pillar-like structure of the FIFA World Cup is presented below as holding the aspiration with which the 32-fold pattern is associated. It can perhaps be compared with a cup whose form is so fundamental to religious ceremonies, itself inviting structural insights (Complementary visual metaphors of "Chalice", 2011; In-forming the Chalice as an Integrative Cognitive Dynamic, 2011). Such designs can be explored as echoed in the forms selected to reflect the culmination of strategic endeavour through traditional iconographic use of the laurel wreath (Game-playing, bull-leaping and laurel wreaths, 2014; Winged logos, laurels and strategic uplift, 2020). The animation below left is an exercise in representing nested significance.

Stack C alternative renderings			Compact visual analogues to vertical arrays
Non-transparent	Rainbow lighting	Transparent	FIFA World Cup	Chalice cup	Laurel wreath

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