We're doing some pedagogy today, meaning mapping out more of the graph, such as filling in a picture connecting Ken Kesey and his Merry Pranksters to Russell Towle, a zonohedron master. They were not intimately connected, more adjacent, same neck of the woods. Russell was in my network.
STEM-wise we have two lesson plans (flight plans) under discussion:
- the density of the CCP (cubic close packing) using S3 (Synergetics Constant) to make a ratio of S3 times XYZ ball volume, divide by six, its domain's volume, that of the "spheric" or rhombic dodecahedron. Answer: about 74% full, 26% empty.
- the dimensions of the six Vanes, we call em, in our homebase tetrahedron, the "gossamer membranes" as we might think of them, sectioning off the four quadrants, congruent isosceles triangles with an included angle of about 109.47 degrees, or acos(-1/3) to be precise.
The two plans go together in that the homebase tetrahedron is defined by four CCP balls, intertangent, of radius R and diameter D.
Those Vane dimensions give a D-edged tetrahedron say of edges 1 (so R = 0.5), with four center-to-corner spokes of about 0.61237, or sqrt(6)/4 to use a symbolic expression. Our segue here is to the A module of Synergetics, where all these lengths and angles come into focus.
Make any sense?
Russell Towle was aware of my early work and saw I was using a squashed aspect ratio he knew how to fix, as he'd also used POV-Ray. I followed his suggestion and my renderings have looked better ever since.
The term "vane", associated with windmills, also has currency within the Urbit realm, Urbit being a kind of internet-like communication technology with its own shoptalk and indigenous computer languages, higher (Hoon) and lower (Nock).
In Urbit, the operating system kernel Arvo, is in touch with its world by means of vanes. Ames and Clay would be vanes, in charge of networking and the filesystem respectively. I'm not the expert. I had a planet up and running, but then it crashed.
