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Polyhedral Empowerment of Networks through Symmetry

Challenge of network connectivity and networking efficiencies

Polyhedral approaches to social network analysis

Polyhedral networks: designing for robustness and survivability

Epistemic networks, simplicial complexes and polyhedra

Polyhedral dynamics and Q-analysis

Polyhedral theory

Polyhedral computing: optimizing responses to complexity

Polyhedral methods of conjoint analysis

Polyhedral design of computer memory utilization processes

Polyhedral databases: operational significance

Polyhedral patterns: representation of complex numerical abstractions

Polyhedral networks: strategic significance

Polyhedral relationship networks?

Polyhedra-based sense of identity?

Missing link: self-reflexive closure?

Symmetry: competition vs complementarity?

Polyhedral empowerment: "eliciting the sparkle from networks"?

Recognition of curvature as fundamental to a polyhedral psycho-social universe?

References

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Associated with *Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors* (2008), *Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization* (2008), *Configuring Global Governance Groups: experimental visualization of possible integrative relationships* (2008) and References

In the further exploration of the possibilities highlighted in the above-mentioned papers, reference is made here to the current applications of "polyhedral approaches" to networks, their operation, and to their significance for information organization in situations calling for higher orders of efficiency and robustness -- and to the insights offered for new approaches to psycho-social organization.

The main emphasis below has been to indicate fields of study and application which may not necessarily be well-connected, however relevant they may be with respect to any potential psycho-social implications. Given that the concept of "network" has proven over past decades to be as significant as a metaphor for social organization as it has as an analytical framework for the development of such organization, it is possible that the potential of "polyhedra" should be similarly understood.

The basic argument is that in psycho-social usage "network" is relatively unstructured and has not achieved much of what was hoped initially in contrasting it with hierarchical modes of organization. Whilst seemingly quite unrelated, the faces and edges linking vertices of any 3-dimensional polyhedron can be mapped in 2-dimensions as a network (a polyhedral net) -- by "unwrapping" the polyhedron. Studies of social networks show that desirable properties such as robustness and information transfer efficiencies can be achieved with networks that take the form of polyhedra having properties such as symmetry. Symmetrical polyhedra in 3-dimensions are those of greatest aesthetic appeal and are intuitively comprehensible as a whole, despite their possible complexity.

There is therefore a case for considering how, in the light of the various polyhedral approaches (considered below), networks might be "polyhedrally empowered" by using polyhedra as structural (or dynamic) templates. Of particular related interest is the degree to which complex multicriteria decision-making is now dependent on such approaches -- suggesting that the comprehensibility and communicability of a solution to any strategic dilemma might be associated with a polyhedral form reflecting its "goodness of fit" as a pattern in a design sense. This would then have important implications for governance.

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