This component of cosmometry is the most thoroughly researched to date. From ancient philosophers and scientists to today’s advanced application of geometry in engineering and architecture, the “structural” nature of the cosmos has been comprehensively researched and put to beneficial use across many disciplines.
In essence, this is the pure geometry aspect of cosmometry, pertinent to atomic and crystalline forms, standing-wave or interference patterning, and vector-based relationships that define geometric form and matter.
The primary forms of structural cosmometry are familiarly known as the Platonic Solids, giving attribution to Plato’s school in ancient Greece when these forms were first deeply investigated. These are the five fundamental “hedrons” — hedron meaning “face” — the tetrahedron (4 faces), hexahedron (6 faces, the cube), octahedron (8 faces), dodecahedron (12 faces), and icosahedron (20 faces). What is unique about these five Platonic forms is that each one is in symmetrical balance with faces composed of only equilateral triangles (tetra, octa and icosa), squares (cube) or pentagons (dodeca), all of the same size. From this most simple and symmetrical expression of form a vast complexity emerges when they become “transformed” through stellation, truncation, combination, subtraction, distortion, etc.
Another way of looking at the structural nature of the cosmos comes from the insights of Buckminster Fuller. As he delved into his research to understand “nature’s coordinate system” that he ultimately called Synergetics, Bucky observed that what we call geometric forms are actually really only “energy events” that articulate into geometric arrays as vectors of energy cross each other and come into a resonant coherence. The point where vectors cross is called a vertex, multiple points being called vertices. A cube, for example has eight such points which we see as the corners of the cube. In his quest to reframe our mind’s way of thinking about the true nature of nature, Bucky often chose to use different words than have been traditionally applied, such as in the case of the word polyhedron (meaning “many faces”). More fundamental than the face of a form, for Bucky, is the array of vertices (crossing points) that define the shape of the face, and are themselves the result of the intersection of energy vectors. As such, Bucky coined the term “polyvertexia” as a preferred and more accurate description of the structural forms we are familiar with. In the context of cosmometry, this perspective is adopted so as to help engender the perception that all form — whether viewed as structural-geometric, flow-toroidal, or field-patterning — is simply the interaction of energy events in whatever medium it is occurring.
In addition to this understanding, all energy interactions that create geometric forms (whether truly structural or not) can be seen as systems of dynamic tension; multiple energy events held in a resonant relationship by the electromagnetic attraction they have on each other that creates a tensional integrity of form. The word used to refer to this tensional integrity is “tensegrity”. Tensegrity has been found to be the fundamental energetic dynamic that binds atoms into molecules, molecules into matter, and underlies cell membrane structures, the musculo-skeletal systems of humans and animals, celestial gravitational dynamics, and more.
In this section we will explore the primary forms of structural cosmometry: The Vector Equilibrium and the five Platonic forms, and what Fuller refers to as the Cosmic Hierarchy of their innate symmetry. This symmetrical interrelatedness is both beautiful and indicative of the seamlessly embedded nature of the fractal-holographic cosmos. And the remarkable relationship of the Phi ratio found throughout these forms attests to the ubiquitous role of this fractal scaling ratio in the fundamental nature of the spacetime field in its primary expressions of structure, flow and field patterning.
Note: It is not the intent for this website to exhaustively survey the vast study that exists of the platonic forms and their myriad of permutations. What is focused upon, instead, is as much as possible to convey how they exhibit certain properties of the fundamental cosmometry, and how this supports the fractal-holographic premise of a seamlessly embedded cosmometric whole.
To delve more deeply into the vast research of geometric phenomena, see Fuller’s Synergetics*, the comprehensive resource at Wolfram Mathematica, and the many other books and websites available on the subject.
*For a simpler introduction to Synergetics, I recommend starting with Amy Edmondson’s A Fuller Explanation.