In titling this blog entry Polys Framework I'm not meaning to impose restrictions on the name of said package. Let's take a look at a script, the above snippet. Better form would be to explicitly close the file at the end. Better yet, I could use a with statement (Pythonistas take note). OK, fixed it in the source (see test32).
What's interesting is each poly, out of the gate, at birth, has a default canonical volume. The Cube weighs in at 3, its dual Octahedron as 4. Tetrahedron is 1 and so on. Points A-Z have been defined, IVM lattice points, to which the five-fold poly skeletons will be added (Icosahedron, RT, PD).
Right on the same line even, at the moment of birth, you may rescale all the edges and thereby scale the volume. Grow or shrink the new poly to any relative size, given its starting point. The concentric hierarchy is a static structure of default starting points, polys already inter-sized, with further action to follow from there.
In this case, we scale down the canonical volume 4 Octahedron to 3/4 of its usual edge lengths. The resulting red octahedron pokes out of the green cube's six face centers, whereas if unscaled by (3/4) it would have intersected the cube's mid-edges with its own mid-edges.
David Koski did a lot of studies for this one, breaking it down further. My script was a zoomed-out treatment, in terms of details. Here's one of the vZome's he shared over Telegram:
Below is the corresponding rendering, achieved from running the above Python source code within a framework which, behind the scenes, causes scene description language to be written, for POV-Ray, which then renders the described output as a PNG file (by default).
