Circle/Sphere: The Simplest
The most simple object (two vertices), these circles and spheres start everything:
1. The black circles are spheres with all the dimensionality and dynamics suggested by the Planck base units.
2. A horizontal, blue line connects the centers of the spheres on the first line or extension of spheres. The blue line become a red triangle then many triangles all on the same plane. Red lines interconnect three as a plane of spheres unfold. Perhaps the ordering of fourth sphere is off.
3. Immediately as the green sphere stack, the first tetrahedron is projected and then the second and third enclosing a fourth triangle which is the base of an octahedron.
“Line-plane-three-dimensional geometry” may happen in that sequence so the first green sphere would populate as the fourth sphere to be displayed and the red lines would immediately begin to triangulate and begin to display the first tetrahedrons. It is an open, yet important discussion. Obviously, the black and green spheres continue to populate and three tetrahedrons begin to enclose the octahedron. Although the sequencing may be off within this automated GIF originally from within Wikipedia’s review of cubic close packing of equal spheres. Notwithstanding, it captures a possible progression better than anything else currently available.
Tetrahedron: Simpler than the octahedron
The tetrahedron we quickly discover is not so simple at all. It has four vertices, four faces, and six edges. Divide the edges by 2, connect those new vertices, and you have the figure on the right. If you continue to divide by 2, just 202 more times, you will have a rough model of the universe.
The simple octahedron is inscribed with the center of every tetrahedron. In the image on the right, the yellow face of octahedron is exposed; the central triangle in the three other faces are part of the octahedron. The other four faces are internal, facing an abutting tetrahedron.
Octahedron: It’s simple, but complex!
There are six “half-sized” octahedrons in each corner of the octahedron and there is a tetrahedron in each face. There are many two-dimensional internal plates. Outlined in colored tape, the white, red, yellow and blue hexagons are outlined. There are also plates of squares and triangles.
There is a centerpoint of every octahedron which is also the centerpoint of every tetrahedron.
The internal configuration of the tetrahedron and octahedron are not well-known throughout the academic world. With the discipline of biology, chemistry and physics, this fact creates barriers to a deeper understanding of the internal dynamics of spheres.