Potential significance of memorable irregularity?

Eliciting Memorable Spheres and Polyhedra from Hyperspace (Part #8)

It is appropriate to respond to a potential criticism as to why not avoid the convolutions of the force-directed approach by making direct use of known polyhedral coordinates. Whilst this might be a viable approach under some circumstances, the advantage of eliciting polygonal loops, as currently extracted, is that it does not preclude the identification of polyhedral forms which could be cumbersome to derive from data subject to intellectual copyright and proprietary formats.

There is every possibility that polyhedral forms based on much larger numbers of polygonal loops (and cycles) could be detected. The potential systemic significance of such structures merits distinct reflection where these are composed of:

problems, as in the current analysis based on perception of relationships between world problems -- suggesting relevance to current preoccupation with the wicked problems of policy making
strategies, as available from a related data set on global strategies
organizations, as available from related data on relations between international organizations
concepts, as is typical of thematically interrelated international conferences, or even those cultivated as understandings of human development
human values, as potentially available from a related data set
individuals, as currently mined from social media data sets

Rather than the "carpet" metaphor used above, a more relevant metaphor may be associated with current recognition of the need for larger "tents" within which to gather together disparate entities. The metaphor is notably employed with respect to interfaith discourse which is currently proving to be so inadequate to the faith-based conflicts of the world. This argument is developed separately (Global Brane Comprehension Enabling a Higher Dimensional Big Tent? 2011). A charming irony noted there is the inspiration that tent-making offered to the polymath Omar Khayyám -- it being the traditional occupation of his family. Hence the relevance of "stitching" to the approach outlined above (Triangulation, connectivity and "stitching": enabling coherent global system dynamics, 2012).

Significantly missing from the above discussion is the sense of chirality by which polyhedral forms may be distinguished, namely as directed graphs there may be right- and left-handed variants of some of the forms above. This is increasingly important in molecular chemistry where the two forms may have quite distinct properties. As stressed, the arrows included into the force-directed layouts above are there purely to indicate the need for such clarification.

Of particular interest is the relation between memorability and degrees of symmetry, as well as the memorability of some unusual structures with unusual forms of symmetry, such as the Szilassi polyhedron, as discussed separately (Mapping of WH-questions with question-pairs onto the Szilassi polyhedron, 2014).

Animations of Szilassi polyhedron of 7 faces (4 types), 21 edges (12 types), 14 vertices (7 types) [totalling 42=2x3x7; product=2x3²7³] (paired shapes coloured identically; prepared using Stella Polyhedron Navigator)
Folding together of the two complementary nets	Rotation of polyhedron	Screen shot of interactve force-directed version

Given the cyclic loops configured by this approach, of particular interest is the potential systemic significance of the polyhedral configurations which might emerge from the process outlined above. In this respect it is appropriate to recall the very extensive range of polyhedra of different degrees of symmetry, somce being convex and others concave. In the case of the drilled truncated cube (presented below), its use as a mapping framework is discussed separately (Changing Patterns using Transformation Pathways, 2015).

Drilled truncated cube of 32 faces (5 types), 64 edges (9 types), 32 vertices (4 types) [totalling 128=2⁷] (animation prepared using Stella Polyhedron Navigator)
Animation with faces non-transparent	Screen shot of interactive force-directed version