Selection of complementary forms in support of imagination

Topology of a Renaissance stargate of higher dimensionality (Part #3)

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(Metaphorical Geometry in Quest of Globality -- in response to global governance challenges, 2009)

Spheres and Hyperspheres (and globality):

• Eightfold Configuration of Nested Cycles of Cognitive Transformations: meta-pattern of connectivity through a hypersphere? (2012)
• Nature of the "ball" in game-playing and governance (2016)
• Embodying the Sphere of Change: reframing metaphors of the I Ching as a codification of the patterns of change (2001)
• Sphere eversion as guide to the cognitive twist of global introversion? (2013)
• Middle East Peace Potential through Dynamics in Spherical Geometry: engendering connectivity from incommensurable 5-fold and 6-fold conceptual frameworks (2012)
• Spherical Accounting: using geometry to embody developmental integrity (2004)
• Spherical Configuration of Interlocking Roundtables: Internet enhancement of global self-organization through patterns of dialogue (1998)
• Spherical Representation of Icosidodecahedral Net of Strategies: configuring strategic dilemmas in intersectoral dialogue (1992)
• Metaphorical Geometry in Quest of Globality -- in response to global governance challenges (2009)
• Cognitive implication of polyhedron circumsphere, insphere and midsphere in strategic implementation (2012)
• Eliciting Memorable Spheres and Polyhedra from Hyperspace: integrative connectivity of problems, strategies, themes, groups or people (2015)
• Polyhedral Conference Representation as a Catalyst for Innovation (2008)
• Dynamic Exploration of Value Configurations: polyhedral animation of conventional value frameworks (2008)

Tensegrity:

• From Networking to Tensegrity Organization (1984)
• Implementing Principles by Balancing Configurations of Functions: a tensegrity organization approach (1979)
• Transcending Duality through Tensional Integrity (1978)
• Psycho-social operationalization of polyhedra through tensegrity representation (2008)

Möbius strip and Lauburu:

• Psychosocial Work Cycle: beyond the plane of MÖbius (2007)
• Beyond the plane of MÖbius: form and medium in terms of the calculus of indications (2007)
• Cognitive implication of Mobius strip (2011)
• Improvisation in Multivocal Poetic Discourse: Basque lauburu and bertsolaritza as catalysts of global significance (2016)

Klein bottle:

• "Sphering the Circle" (from 2D to 3D): a Klein-bottle relationship "belt drive"? (2007)
• Cognitive implication of Klein bottle (2011)
• Intercourse with Globality through Enacting a Klein bottle (2009)

Polyhedra (in 3D): ****

• regular (Platonic) and semi-regular (Archimedean)-- cube , Rubik
  • Cognitive implication of spherically symmetrical polyhedra (2011)
  • Rethinking Rubik's Cube: a mnemonic device for ways of knowing and engagement? (2009)
  • Interplay of Sustainable Development Goals through Rubik Cube Variations: engaging otherwise with what people find meaningful (2017)
  • Nesting polyhedra to enable comparison of patterns of discourse (2015)
  • Psychosocial Implication in Polyhedral Animations in 3D: patterns of change suggested by nesting, packing, and transforming symmetrical polyhedra (2015)
  • Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors (2008)
  • Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization (2008)
  • Coherent Value Frameworks: pillar-ization, polarization and polyhedral frames of reference (2008)
  • Possibilities of a polyhedral mapping of wisdom? (2012)
  • Polyhedral Empowerment of Networks through Symmetry: psycho-social implications for organization and global governance (2008)
  • Gallery of Polyhedral Flower Arrangements (2014)
  • Emergent polyhedral configuration of alternating systemic functions (2012)
• other (Stewart toroids, Szilassi):
  • Cognitive implication of drilled toroids (2011)
  • Proof of concept: use of drilled truncated cube as a mapping framework for 64 elements (2015)
  • Interactive Polyhedral Mapping onto Drilled Truncated Cube using Force-directed Layout of d3.js (2015)
  • Mapping of WH-questions with question-pairs onto the Szilassi polyhedron (2014)
  • Framing Global Transformation through the Polyhedral Merkabah: neglected implicit cognitive cycles in viable complex systems (2017)
  • Association of the Szilassi polyhedron with cube inversion (2018)

Polychora (N-polytopes), polyhedra (in 4D):

• Cognitive implication of tesseract and related uniform polytopes (2011)
• Comprehending the shapes of time through four-dimensional uniform polychora (2015)

Helices and spirals:

• Helices:
  • Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity -- Eppur si muove: Biomimetic embedding of N-tuple helices in spherical polyhedra (2017)
• Euler spiral / Clothoid:
• Tao ??? spiral
• Vortices:
  • Reframing a strategic attractor as a vortex involving a "cognitive twist" (2014)

Torus (and halo):

• Cognitive implication of  toroidal forms and dynamics (2011)
• Toroidal configurations as fruitful loopery (2015)
• Toroidal cognitive container? (2011)
• Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8) (2006)
• Toroidal mappings of wisdom questions and answers (2012)

Cardioid

• Symbolizing Collective Remembering Otherwise: encompassing the "headless hearts" and "heartless heads" through their dynamic entanglement (2018)
• Interpretation of the heart pattern via the coaction cardioid (2018)

Poincaré disk:

Mandelbrot set renderings:

knot ***

phase ***

water ***

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