Excerpt from a posting titled, On Constructing the Universe From Scratch This animated illustration is from Wikipedia. It demonstrates how spheres generate lines (lattice), triangles, and then a tetrahedron. With that second layer of green spheres emerges the tetrahedraloctahedral couplet. The discipline, known as cubic close packing (ccp), deserves our attention. “The Kepler conjecture states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular. This conjecture was proven by T. C. Hales.” (Wikipedia) Also see: 

Category: Combinatorial Geometry
Are the first 67 notations key missing links?
Could an integrated Universe View^{1} open new approaches to old academic questions? Because it redefines our understanding of space and time, it seems to open that possibility.
Sir Isaac Newton’s space and time became an absolute frame of reference^{2} and the basis of commonsense logic for well over 300 years. But, what if space and time are derivative, discrete and quantized? What if both have a specific beginning, the Planck Base Units, and today’s current timelengthmasschargetemperature of the universe, or the Now, are always the endpoints? What if every notation is a highlyintegrated part of the whole?
There are just over 200 base2 exponential notations from the Planck Base Units to this moment, your “today.” That range is best defined as the Age of the Universe.
Within our Universe View, also known as Universe Table and Big Boardlittle universe, the first 67 doublings cannot be measured at the singularity of the Planck base units. Planck time cannot even be measured at the 67th doubling. Though driven by a simple logic, simple mathematics, and very simple geometries, those first 67 doublings per se are not part of our observed universe and are currently not part of academic analyses.^{3}
Given this situation, we advocate that the nature of space and time be reopened for scrutiny in light of these first 67 steps. Could these steps be the missing links that open real pathways to new insights into historic, impossiblydifficult and persistent, unanswered, academic questions that exist across all the disciplines? To open such a discussion, brief summaries and a few links will be provided within some of those large categories of human endeavor. Eventually indepth articles for each will be written and linked from here:
 Physics. Because the Big Boardlittle universe defines parameters and boundary conditions for everything, everywhere throughout all time, it could become some kind of a front door to the theory of everything.
 Mathematics. These 67 steps just may be the mathematics, geometries, and logic that give rise to the physics of particles and waves. Here continuity equations are extended to the limits of universe. An entirely new infrastructure for symmetries is opened.
 General sciences. These 67 steps provide new ways of looking at tilings and tessellations, and periodicity and frequency. All the sciences are necessarily linked and causal determinacy is extended throughout the entire universe (A new article will be written but go here for tilings and tessellations.)
 Cosmology. By the 67th step or doubling, although an unmeasurablyshort duration, 1.591 ×10^{−23} seconds, the amount of complexity has become so great, Lemaître’s Big Bang Theory could possibly be gently deflated for a more Quiet Expansion.
 Philosophy. Here too the 67 notations may be the bridges and conduits between the historic debates about the finite and the infinite, between the perfect and imperfect, and between subjects and objects. If all the Planck base units are finite, what is infinite? The easy and quick answer based on the question, “What is perfect?,” we answer ordercontinuity, relationssymmetries and dynamicsharmonies. These forms and functions appears to be the most simple definition of that which is perfect and infinite. That which is imperfect and finite, would be defined initially by the five Planck base units, yet more specifically the five units as defined within notation 67.
 Ethics. Within our working definitions of the infinite and the perfect are ethical foundations that are necessarily related to the sciences, mathematics, business and religions.
 Politics. Can the historic debate between DemocratRepublican, liberalconservative, communist (socialist)capitalist be reduced to a question of wavesparticles and subjectsobjects? Can both be accused of misplaced concreteness? Do the first 67 steps suggests a model whereby the hyphens are the really real? The hyphens, or the relations or the ratios, pull everything everywhere for all time into a dynamic, a thrust of the current moment, to order by creating continuity, to relate by creating symmetries, and to interrelate by creating harmonies. A primary article will be forthcoming.
 Religion. Though introduced within the section about philosophy and ethics, religions requires special study. Too much chaos throughout the world is created by religious beliefs with no grounding in the universe; these beliefs exist only in the minds of the believers. Another article that goes in greater depth will be forthcoming.
 Brain/Mind. Although the brain is located in the skull, the location of the mind is entirely open. Within the first 67 notations, just prior to first physical expressions of the Planck base units, a special case of nonlocality is defined whereby it has been postulated within the Universe Table that the mind is located within a set of notations, Systems, which have been postulated (imputed or hypostatized) to include notations 50 to 60.
The longstanding goal of this article is to open the discussion to explore how these statements could be true and in what ways they are not true.
We invite you to join us to determine if and how these 67 notations just might be the infrastructure within which ageold questions can be addressed in new ways.
Endnotes, Footnotes, and References:
1. We have begun building a bridge to the 68th notation, the place where things begin to be measured in space and time. We will be using all the current research at research labs such as CERN, and speculative work such as the Langlands programs and amplituhedrons. Pi, all the dimensionless constants, the physical constants, pure geometries, and numbers and ratios will all be used in new ways.
This article is our appeal for help.
2. Sir Isaac Newton’s space and time became an absolute frame of reference
3. Within those first 67 notations are a different set of building blocks for the universe. If we bring to bear all of the geometries (projective, analytic, combinatorial..), including the simplest geometries (cellular automaton and the platonic solids), a little bifurcation theory and the 80known binary operations, perhaps we can begin to intuit how forms become structure, then substance, then qualities, relations and systems, increasinglyandexquisitely complex with literally trillionsupontrillions of possible combinations and expressions, right on up to the fermions, bosons, skyrmions and all combinations of elementary particles that make up the Standard Model (SM) and the SMPP for Standard Model for Particle Physics.
Much more to come: Entropic forces and causal determinacy
Tetrahedrons & Octahedrons
The text within the picture reads as follows:
Three levels of simple complexity:
1. Observe the tetrahedron in the bottom left corner.
2. Notice that it is enclosed in a larger tetrahedron. Right beside is
an octahedron, plus there is a tetrahedron in each of the other three corners. Every tetrahedron encloses four halfsized tetrahedrons and an octahedron.
3. Notice that our larger tetrahedron is enclosed by an even larger tetrahedron. This pattern repeats itself getting smaller and getting larger. Part of the complexity can be seen by observing the center octahedron. Notice the red, black and blue hexagonal plates. A white plate has been obscured.
For more, please follow this page on the website:
https://bblu.org/2014/12/01/tiling
“Tiling the Universe in 201+ Exponential Notations:
The Great Chain of Being”