Polyhedral implications for cognitive governance understood in global terms?

Optimizing Web Surfing Pathways for the Overloaded (Part #4)

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The argument here is a development of previous preoccupation with the polyhedral organization of institutions and issues in a global context (Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors, 2008; Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization, 2008).

Of particular relevance is the possibility that networks of organizations active in cyberspace might be more fruitfully organized in polyhedral form in order to enhance their collective integrity and viability, as discussed separately (Polyhedral Empowerment of Networks through Symmetry: psycho-social implications for organization and global governance, 2008). Similar arguments can be made with respect to the thematic preoccupations of such networks, interrelated as they are through patterns of discourse (Spherical Configuration of Interlocking Roundtables: Internet enhancement of global self-organization through patterns of dialogue, 1998).

In this light, the focus with respect to the web user, vulnerable to overload, is the form a polyhedral organization of sets of websites might take to enhance the regular browsing experience -- for that user. Given the parallels highlighted above to computer memory organization, the implications of "overload" in both cases merit comparison. Additionally, would the pattern so configured constitute an integrative mnemonic clue to the associated preoccupations? Such "tricks" are characteristic of the skills reported by participants in competitions like the World Memory Championships.

The early use of a webring (mentioned above) offers a clue to more integrative organization. The simpler symmetrical polyhedra are notably characterized by interlocking great circles variously passing through polyhedral nodes, understood here as websites.

Platonic polyhedra (regular) (reproduced from Wikipedia)
Polyhedron		Vertices	Edges	Faces	Schläfli symbol	Vertex config.
tetrahedron		4	6	4	{3, 3}	3.3.3
hexahedron (cube)		8	12	6	{4, 3}	4.4.4
octahedron		6	12	8	{3, 4}	3.3.3.3
dodecahedron		20	30	12	{5, 3}	5.5.5
icosahedron		12	30	20	{3, 5}	3.3.3.3.3

The possibility indicated by the above polyhedra is that, according to the number of websites to be regularly visited, their vertices could be used to map the sites. The edges would then be indicative of possible link pathways between them. More complex patterns, suitable for mapping a larger number of websites, are indicated by the following table from Wikipedia, however especially relevant is another Wikipedia table (List of uniform polyhedra by vertex figure).

Archimedean polyhedra (semi-regular) (reproduced from Wikipedia)
Name (Alternative name)	Schläfli Coxeter	Transparent	Solid	Net	Vertex figure	Faces		Edges	Vertices
truncated tetrahedron	{3,3}	(Animation)			3.6.6	8	4 triangles 4 hexagons	18	12
cuboctahedron (rhombitetratetrahedron)	r{4,3} or rr{3,3} or	(Animation)			3.4.3.4	14	8 triangles 6 squares	24	12
truncated cube	t{4,3}	(Animation)			3.8.8	14	8 triangles 6 octagons	36	24
truncated octahedron (truncated tetratetrahedron)	t{3,4} or tr{3,3} or	(Animation)			4.6.6	14	6 squares 8 hexagons	36	24
rhombicuboctahedron (small rhombicuboctahedron)	rr{4,3}	(Animation)			3.4.4.4	26	8 triangles 18 squares	48	24
truncated cuboctahedron (great rhombicuboctahedron)	tr{4,3}	(Animation)			4.6.8	26	12 squares 8 hexagons 6 octagons	72	48
snub cube (snub cuboctahedron)	sr{4,3}	(Animation)			3.3.3.3.4	38	32 triangles 6 squares	60	24
icosidodecahedron	r{5,3}	(Animation)			3.5.3.5	32	20 triangles 12 pentagons	60	30
truncated dodecahedron	t{5,3}	(Animation)			3.10.10	32	20 triangles 12 decagons	90	60
truncated icosahedron	t{3,5}	(Animation)			5.6.6	32	12 pentagons 20 hexagons	90	60
rhombicosidodecahedron (small rhombicosidodecahedron)	rr{5,3}	(Animation)			3.4.5.4	62	20 triangles 30 squares 12 pentagons	120	60
truncated icosidodecahedron (great rhombicosidodecahedron)	tr{5,3}	(Animation)			4.6.10	62	30 squares 20 hexagons 12 decagons	180	120
snub dodecahedron (snub icosidodecahedron)	sr{5,3}	(Animation)			3.3.3.3.5	92	80 triangles 12 pentagons	150	60

Of further interest is then the order in which these links (indicated by the edges) are traversed by the user within the pattern provided by a given polyhedron. Furthermore, also of interest is the regularity with which given sites are visited within the pattern -- with possible significance to be found in the symmetrical "regularity" of the Platonic polyhedra and the "semi-regularity" of the Archimedean polyhedra. A further issue is the direction in which links are traversed through the pattern -- in terms of chirality.

There are of course numerous other polyhedra with various properties which may trigger insights into their potential relevance for patterning web browsing. Some may prove of greater relevance to enhancing integrative comprehension of the thematic content of the pattern. Personal preferences may come into play with respect to memorability -- even including unusual polyhedra with lower degrees of symmetry (as indicated below). Patterns of greater abstraction may be of even greater relevance to exploration of contexts for some form of cognitive fusion as argued separately (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006).

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