Coherent global mapping of virtues and sins?

Values, Virtues and Sins of a Viable Democratic Civilization (Part #13)

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The question is then how the earlier experiment in representation with polyhedra -- especially the cuboctahedron -- can be usefully applied to the sets of virtues and sins -- as a prelude to reframing the relationship between constructive and destructive values (Memorable representation of the dynamics of a hyper-wealth complex, 2022; Topology of Valuing" dynamics of collective engagement with polyhedral value configurations, 2008).

The case for presenting values in this way has been discussed separately (Embodying Values Dynamically through Alternation: integrating sets of polarized static values through indicative metaphor, 2008; Dynamic Exploration of Value Configurations: polyhedral animation of conventional value frameworks, 2008). Extracts from the latter are reproduced below.

Animated mappings of polyhedral representation of value configurations: a challenge to integrative imagination screen shots of stages in the transformation of the geometry of sets of values
European Convention on Human Rights	Universal Declaration of Human Rights	Arab Charter on Human Rights
18 Articles displayed on 2 face-types of a rhombicuboctahedron	30 Articles displayed on 1 face-type of a rhombicosidodecahedron	53 Articles displayed on 2 face-types of a rhombicosidodecahedron
Animations made using Stella Polyhedron Navigator

With respect to virtues and vices, a point of departure is to make use of the cuboctahedron as shown below (left), in the light of the previous exercise (Memorable representation of the dynamics of a hyper-wealth complex, 2022). That particular polyhedron is especially useful because it offers 3 opposing quadrilaterals and 4 opposing triangles. These can be used respectively to map 3 theological virtues (and their opposing sins), and 4 cardinal virtues (and their opposing sins). Arguably the configuration then offers a framework enabling exploration of their systemic relationships from an integrative perspective.

Animated mapping of 7 virtues and 7 vices onto opposing faces of a cuboctahedron
Animations made using Stella Polyhedron Navigator

The cuboctahedron has been the subject of extensive commentary from a systemic perspective, most notably by Buckminster Fuller (Synergetics: explorations in the geometry of thinking, 1975). However, despite the cognitive emphasis implied by the title,the relevance to strategic "thinking" is less than evident, as discussed separately  (Geometry of Thinking for Sustainable Global Governance: cognitive implication of synergetics, 2009).

The rhombic dodecahedron is the geometrical dual of the cuboctahedron, meaning that the polygonal fields configured by the latter are transformed into the vertices of the former. This offers the contrast between virtues-values as semantic "fields" and their comprehension as "points" -- then more suggestive of their recognition as principles. This alternative representation of the polyhedral configuration above is presented below.

Animated mapping of 7 virtues and 7 vices onto opposing vertices of a rhombic dodecahedron
Animations made using Stella Polyhedron Navigator

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