Friday, October 12, 2018

Welcome to "Sesame Street"

Another Vintage Atom

As a way of embedding a cultural icon, influential on me among many, I've oft referred to a certain "concentric hierarchy" as "the Sesame Street of Synergetics".

I'm of course talking about a "stack" of concentrically arranged (one could say layered) topological frameworks, Eulerian networks.

You may think in terms of great circles and how we used to imagine electrons flying along geodesics, in those ancient movies about "the atom".  That's the kind of mental imagery we encourage, even if we're not literally talking about an atom.

The great circles remain, absent any specific frequency or special case interpretation.

However, the strobe light may reveal a shape at a "stand still" that's more what we might have grown up calling "Platonic".  When spinning around any pair of poles, we get a readout.

A lot of schools left those out (the Five Platonics), so if you don't know what a tetrahedron is, you're in good company.

After a few Sesame Street level videos, some time with puppets, some hands-on time exploring tactile senses (Gibbs-ish ala solid, liquid and gas), you'll be clear not only on what a tetrahedron is, but several other such hedrons (or hedra) as well.

You'll be ready for kindergarten in no time!

Not that your vocabulary needs to get that big right away.  Keep watching, stay tuned.


Two tetrahedrons intersecting, give a cube, its dual the octahedron, their pairing a dodecahedron of diamond faces, space-filling (and not Platonic).

Said RD has volume 6 with respect to said cube (3) and tetrahedron (1), octahedron (4).

The dual of the RD, the VE (cuboctahedron), scales to bridge the twelve centers of closest packed unit-radius spheres to:

(A) their nearest neighbors and
(B) to a shared nucleus.

1, 12, 42, 92... a lot of you know this already.  The tetrahedron connects four of such spheres and serves as unit.