From a sphere to many spheres to a tetrahedron

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 tetrahedral-octahedral 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:
The horizontally-scrolled chart of all 201+ notation
Quiet Expansion of the Universe
An index of related postings
The homepage for this project

Sphere to tetrahedron-actahedron couplet
Attribution: I, Jonathunder
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