Reframing NATO and The Pentagon?

Envisaging NATO Otherwise -- in 3D and 4D? (Part #4)

NATO: At the time of writing, with new strategic directions of NATO as a principal theme of the presence of Donald Trump at a NATO Summit, the approach explored previously with respect to the Star of David and the Merkabah may also be explored with respect to the symbol with which NATO is identified (Framing Global Transformation through the Polyhedral Merkabah: neglected implicit cognitive cycles in viable complex systems, 2017). This can be illustrated by the images below.

The NATO symbol or logo is necessarily in 2D (A Star is Born: choice of design, 2016). The question is whether the geometric extension of the NATO logo into 3D would enable recognition of "missing strategic dimensions" -- whatever this might imply in strategic terms. Just as the 2D depiction may be assumed to reinforce certain cognitive processes, would the reinforcement of a more complex set of processes be reinforced -- of greater relevance to global governance?

The previous discussion argued for the value of basing this design on a four-fold augmentation of a fundamental central polyhedron, namely the tetrahedron -- informally named the augmented tetrahedron, composed of 5 tetrahedra. Each tetrahedron, as the most fundamental polyhedron, could be understood as embodying one of the 5 fundamental values of NATO, and of the Europe it is designed to defend: Democracy, Freedom of speech, Freedom of the media, Independence of the judiciary, Protection of minorities. These were reaffirmed by NATO Secretary General Jens Stoltenberg (NATO's Enduring Mission -- Defending Values, Together, NATO, 8 September 2016).

The augmented tetrahedron depicted below is composed of 12 faces (of 1 type), 18 edges (of 2 types) and 8 vertices (of 2 types). It can be understood as composed of 5 tetrahedra.

Juxtaposition of NATO 2D symbol with views of augmented tetrahedron in 3D Reproduced from Framing Global Transformation through the Polyhedral Merkabah: neglected implicit cognitive cycles in viable complex systems (2017)
NATO symbol		Screen shots of 3D augmented tetrahedron ( variously rotated)
design in 2D	schematic in 3D?

	Images prepared using Stella Polyhedron Navigator

Curiously, but perhaps appropriately, the 3D form recalls that of the morning star spiked club of medieval times -- of which a variant, as a mace, is now a central feature of some parliamentary ceremonies. The structure also resembles that of certain types of road traffic spike deployed by security services.

The Pentagon: Given the fundamental strategic importance of The Pentagon (as headquarters of the US Department of Defense) with respect to global security -- understood in terms of full-spectrum dominance -- there is a case for extending the above exploration in terms of the 5-fold symmetry of that body as a symbol. As noted, the augmented tetrahedron, indicated above as a means of depicting NATO otherwise, is composed of 5 tetrahedra, one of which is central to the configuration.

This suggests the possibility combining 5 such tetrahedra otherwise in what is known as a tetrahedron 5-compound (with 20 faces, 30 edges and 20 vertices). The vertices of the compound then form the 20 vertices of the dodecahedron. It is one stellation of the regular icosahedron. The compound is unusual in that the dual figure is the enantiomorph of the original. If the faces are twisted to the right, then the vertices are twisted to the left. The compound has been extensively studied by geometers, notably as a geometric illustration of the notion of orbits and stabilizers; it is one of five regular polyhedral compounds. Two such tetrahedron 5-compounds of opposite chirality combine to make a tetrahedron 10-compound (with 40 faces, 60 edges, and 20 vertices).

Symbolic reframing of The Pentagon? Alternative views of the compound of 5 tetrahedra

Images reproduced from Wikipedia

Such structures in 3D (with geometry reflective of the number of members of NATO, for example) are an indication that the conventional simplicity of the Pentagon as a symbol may be inherently misleading.