Pretty Polys

More Dev Notes

Kirby Urner
5 min readApr 17, 2022


That’s “dev” as in “curriculum dev” i.e. a role wherein you might be employed filling Github repos with Jupyter Notebooks.

The product is open source but the glory goes to those who did the work, which includes funding the effort, having the foresight to do so.

I’m talking about elements of my School of Tomorrow in my case. You may be developing a your own pet project, as a curriculum dev, seeking sponsors and everything. A long time before this, I did some similar work through McGraw-Hill.

Perhaps you saw the movie: The House of Tomorrow (yes, there’s also a book).

early prototype, Henry Ford Museum

The grandma character is caring for a grandson who’s parents died in a crash or something. She was a huge Bucky fan in her day, and is more than tinged with the associated fanaticism. She insists her ward be home schooled (in a geodesic dome what else?) and learn the kind of stuff Buckminster Fuller would want him to know, to become “a Design Scientist”. Yes, they make movies about just about anything these days.

the movie (based on the book)

I’m in no position to indulge fantasies about World Game in a box, or textbooks in a vacuum. I need to connect with existing curricula to keep it real, and in the Silicon Forest that means something like an Algorithms and Data Structures class, but at a before college level (meaning high school and accelerated middle school).

Private schools specializing in the special needs of the precocious often copy each other, especially when invited to so so per a shared open source ethos. In gaining followers and garnering imitators, I’m contributing to a sense of school pride, something all schools seek to stoke.

So is there anything that specifically Buckyian in what I’ve done? The diehards among you might be thinking a went with the Concentric Hierarchy or something, and that’s exactly what I did. Anchoring a curriculum, at least in one corner, with the Platonics, is just a smart way to go. Yes, I’m talking Polyhedrons, yet I remain open to new semantics.

memory holed toy

What are we doing with Polyhedrons then? Well of course putting them into a relational database, and then reconstituting them as Objects.

Having a computer language such as Python at our fingertips helps capture the “Polyhedron as type and sub-types” architecture (not the only one feasible of course, but one worth including).

The parent somewhat abstract class (in terms of generic algorithms, not in the computer science “abstract class” sense) knows how to rotate, scale, translate a self (a Polyhedron).

The sub-types of Polyhedron know their own Faces (Tetrahedron has four) and these get defined by Edges going around in a “circle” (minimally a triangle in this world).

Edges, in turn, are defined by pairs of Vertexes.

These come pre-labeled and pre-stored, in XYZ and/or Quadray (IVM) terms.

CCP coordinates

A word of explanation here:

IVM was Bucky’s abbreviation of “isotropic vector matrix”, a scaffolding interconnecting unit radius balls in a CCP (cube centered packing).


“Quadrays” names a vector algebra apparatus for casting XYZ coordinates as 4-tuples relative to the four arrows (rays) of a tetrahedron instead.

Just think of a caltrop instead of a jack, as your basis for vectorial geometry.

Four Ray Origin
Six Ray Cartesian Origin

In the process of making our Polyhedrons in Python (or other OO language) we also nest them and discuss their relative volumes. Here, then, is our obvious branch point, to where we’ll venture into a different notion of a unit of volume, aside from the cubical one, of edges one. American history suggests we pioneer here.

Why not a tetrahedron instead, for our volumetric unit? What would be the ramifications?

That’s the Buckyian part: exploring the consequences of shifting more weight onto the tetrahedron. Undertaking such explorations does not entail losing our grip on what we already know.

Concentric Hierarchy (CH)

My actual repos (git repositories, archival sandboxes) are not that tied together yet though, in that my SQLite database of Polyhedrons comes together with Jupyter Notebooks and pandas volume tables only across several exhibits, never unified as one.

Only the rare teacher would spontaneously connect the dots and see the bigger picture, including even the relevance of the Quadray Coordinates piece of the puzzle. So I have my work cut out for me then.

Most would want a lot more time and explanations to grok these details, and I don’t blame them. That’s where my Youtube channel comes in, perhaps in addition to whatever live engagements.

For those who get it early, the benefits of being a first kid on the block (at least in your neck of the woods) may be considerable.



Kirby Urner