Unusually memorable mapping possibilities of a tetrahedral geodesic sphere

Refining the Value of Sustainable Development Goals (Part #8)

---

[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]

---

Another highly unexpected polyhedral form, cited with respect to its 34 vertices (in the table above), is especially unusual in this context in having 64 faces. The process of (un)folding between 2D and 3D offers insights in contrast to the rotunda form above (as illustrated on the right below).

Indications of 4-Frequency tetrahedral geodesic sphere -- with (un)folding animation (34 vertices of 4 types; 64 faces of 6 types; 96 edges of 8 types; )

Contrasting views indicative of the complex sysmmetries of the 4-Frequency tetrahedral geodesic sphere
Images generated with Stella Polyhedron Navigator

In the light of the assumption that the 17 value-goals necessarily exclude those by which they are opposed, the polyhedron may be explored as a globe of which only one half is strategically "visible". With the value-goals as vertices, 17 of these may be selectively coloured (black in the examples below) to suggest that "visible" domain -- as distinct from those which are "hidden" by the curvature of the globe, as understood cognitively. Associated faces may also be distinctively coloured. Associated faces can also be coloured (and labelled) as recognized zones, in contrast to those which are hidden.

Marking of 17 "visible" vertices with the implication of 17 "hidden vertices"
Images generated with Stella Polyhedron Navigator

The 64 faces invite a complementary mapping exercise of significance in terms of the classical insights of Chinese culture -- usefully recognized as having embodied a systematic understanding of sustainable development into the patterns of interaction encoded by the 64 hexagrams of the I Ching (Transformation Metaphors derived experimentally from the Chinese Book of Changes (I Ching) for sustainable dialogue, vision, conferencing, policy, network, community and lifestyle, 1997).

This complex pattern of interacting conditions can be mapped onto the faces of the polyhedron -- whether as the classical hexagram code or with the corresponding Chinese idiogram. The pattern of 64 is nearly unique within that polyhedral context. However one interesting candidate is the toroidal drilled truncated cube with 64 edges -- with which any set of 64 elements could be associated, as previously explored (Proof of concept: use of drilled truncated cube as a mapping framework for 64 elements, 2015). In that exercise the edges were labelled. The complementarity with the 34 value-goal dynamics merits further exploration.

Mapping of 64 conditions of I Ching onto 4-Frequency tetrahedral geodesic sphere (images attributed randomly, not meaningfully)
Animation of hexagram mapping	Animation of idiogram mapping
Animations generated with Stella Polyhedron Navigator

---

[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]