(June 12, 2021): Inherent relationships of the newly discovered irrational values that define the wave intersections of a Torus appear to define all geometric relationships for Platonic Solids (at least) and I believe all polyhedra/Polytopes.
In this example, the numerical positions demonstrate direct linkage to √3 family of values: Root3, Root2.25, Root 8.25 and Root12. (√12 / √3 = 2; √8.25 / √2.25 = (√3 -1 / 2)*10; √2.25 / √3 = √3 / 2). Together, their vectors form a perfect Icosahedron. Is this the structure, as many physicists believe, that represents the entire Universe (in scaling fractal emanations)?
The Dodecahedron is made from the wave intersections defined by Wave Intersection values defined as (10*√e) -1 / √2.16 = 3; √1/.864 / √2.16 = (√3)-1; √2.16 / (√.84 + 1)^2 = .4 …..it is very exciting to see how the Universe perceives the construction of its Polyhedra/Polytopes. “Ratios of Ratios”.
My conclusion: We exist in a purely ratio-based Conscious Universe. Measurement values (that we believe to be entirely arbitrary and yet they absolutely are ratio based constants (themselves) of Consciousness as well –eg: 6 – e = 1 Meter; 5 – 1 Meter = 1 Royal Egyptian Cubit; and 6 – 5 = 1 Foot; and 6 = 1 FathoM (Father/Mother backwards) and therefore do not matter beyond their ratio value versus everything else.
The universe is becoming conscious, that is why it is constantly changing. It is not a finished product, it is a work in progress. It is designed with a proportional model of constant combinations and permutations. Learning or awareness is done through natural algorithms, which is what you are discovering with your beautiful geometric figures. Many successes and enlightenment !!!