Interrelating global cycles of dramatic situations

Thirty-six Dramatic Situations faced by Global Governance? (Part #12)

Global systemic forces? The polyhedra indicated above are variously a potential source of insight into ways of thinking about the forces engendering dramatic situations as illustrated by the animations below. The alternatives invite discussion as to whether it is the edges the drama is engendered by the edges (as "red lines"?), , by the faces (as "tectonic plates"?), or by the vertices (as critical points or "tipping points"?).

Alternative perspetives on forces potentially engendering dramatic sistuations
Stella octangula (un)folding 36 edges; 24 faces; 14 vertices	3-Frequency tetrahedral geodesic sphere (alternating between 2 conditions) 24 edges; 36 faces; 20 vertices	Leonardo octahedron (un)folding 96 edges; 48 faces; 36 vertices

12-sided "table" in 3D: One exercise to that end could be formulated in terms of Increasing the dimensionality of the archetypal Round Table? (2018). That possibility was explored in terms of envisaging a 12-sided (dodecagonal) table in 3D. Given the dramatic implications of the traditional 12-sided Round Table, consideration can be given to a dodecagonal table and its projection into 3D -- and what this might then imply for enhanced modes of discourse.

The following animations of unusual polyhedra, derived by further truncation from the truncated cube, were discovered in relation to the communication implications of great circles in connection with different polyhedra (Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity, 2017). However, in order to reproduce that configuration so as to explore the great circle process, it proved necessary to construct in 3D a cubic arrangement of dodecagonal faces (right-hand image below).

Animations of variants of truncated cube with dodecagonal faces		Framework of dodecagonal faces

Reproduced with permission from The Truncated Cube, with Two Variations Featuring Regular Dodecagons (RobertLovesPi's blog, 2016)		Constructed by use of Stella Polyhedron Navigator and X3D-Edit

Given the importance conventionally accorded to a 12-fold patterns of dialogue, most notably in round tables of the wise and in juries, the question explored by the great circle process was the potentially implied pattern of interactions. Three sets of 12 great circles were therefore applied to the dodecagonal framework. This was done as a possible prelude to introducing a 12-fold helical pattern as discussed in relation to the Triple Helix model of innovation and suggestions for a Quadruple and Quintuple variants (Embedding the triple helix in a spherical octahedron, Embedding the quadruple helix in a spherical cube, Embedding the quintuple helix in a spherical dodecahedron and a Pentagramma Mirificum, 2017).

The more complex variants necessarily address strategic issues of greater complexity (Elias Carayannis and David F. J. Campbell, Triple Helix, Quadruple Helix and Quintuple Helix and How Do Knowledge, Innovation and the Environment Relate To Each Other? International Journal of Social Ecology and Sustainable Development, 1, 2012).

As indicated below, the 36 great circles create a complex interweaving pattern in their own right, possibly precluding addition of helical patterns (or implying them in some way). As to any emergent symbol, this might be better understood as taking a 3D form (rather than 2D, as in the cases above). Given that any of the Kepler-Poinsot star polyhedra could be considered too complex, a better symbol might be the 8-vertex compound of two tetrahedra (otherwise known as Stella Octangula), and discussed separately with respect to the Merkabah as a 3D variant of the Star of David (Framing Global Transformation through the Polyhedral Merkabah: neglected implicit cognitive cycles in viable complex systems, 2017).

Successive addition of 36 great circles to dodecagonal-faced cubic framework (above-right)
Application of 1st set of 12 great circles	Application of 2nd set of 12 great circles	Application of 3rd set of 12 great circles


Patterns dynamically combining red / green / blue circles are shown in the animation. Interactive 3D versions: x3d; wrl/vrml. Video: mp4 (7mb)

Use of a dodecagonal-faced truncated cube pattern is especially interesting for mapping purposes in that 72 edges are subtended by the 36 great circles. However 8 of these edges are associated with two great circles, offering 64 edges for distinctive mapping. A further 24 edges are excluded from this encirclement. The pattern of 72 edges recalls the traditional symbols articulated as the contrasting qualities of the angelic order on the one hand, and the demonic order on the other, as discussed separately (Engaging with Hyperreality through Demonique and Angelique? Mnemonic clues to global governance from mathematical theology and hyperbolic tessellation, 2016; Variety of System Failures Engendered by Negligent Distinctions: mnemonic clues to 72 modes of viable system failure from a demonic pattern language, 2016).

Structurally consistent with the 3D structure of the dodecagonal configuration (based on the truncated cube) is that of the drilled truncated cube (discussed above), unique in its pattern of 64 edges (Proof of concept: use of drilled truncated cube as a mapping framework for 64 elements, 2015). As discussed there, this offers a 3D mapping surface for the 64 distinctions made by the I Ching encoding or the genetic codon combinations.