Per content in my Youtube channel, on Medium and so on, I've seen Cascadian Synergetics entering local systems through the open Silicon Forest portal. The architect in Bucky left us a computational geometry, something to sink our teeth into by means of computer programs. Simple ones. One or two liners in some cases.
This is because of our focus on the CCP, a well-known lattice in crystallography and in mathematics more generally. Other distinct meanings of CCP might get in the way, as name collisions, minus an ability to think in terms of namespaces, a faculty Python provides, Python being an open source, free computer language. We might say OSF instead of FOS sometimes.
The CCP may be described in terms of a growing arrangement of layered balls, typically fruits or cannon balls in the textbooks. Concentric layers in a cuboctahedral conformation is the trademark Synergetics way of showing it, giving the cuboctahedral number sequence per OEIS: 1, 12, 42, 92, 162... That's one line of code in Python.
What grade levels are we talking here? In my working model, that's up to faculty designers at the individual school level. Curricula typically employ "spiralling" meaning a topic is re-encountered at different levels, not "once and for all" in some strictly linear sequence. Topics get revisited, coming from different angles sometimes.
I'd see the power law, freed from any exclusively square-cubic context, introduced early: that area and volume increase or decrease as a 2nd and 3rd power of a shape's linear dimensional increase or decrease. Introduce phi-scaling i.e. a linear grow-shrink ratio (factor) of ~1.618 or ~0.618, phi's reciprocal.
To these linear changes there correspond scale factors of phi to the 2nd and 3rd power, for computing the new area and volume respectively.
Starting with a shape known as the S module in Synergetics, we scale it up by phi, getting a new volume of S times phi to the 3rd power. Scale up this new larger volume's six edges by phi and get S times phi to the sixth power. S3 + S6 = 1, is one way to abbreviate the result, where 1 is likewise the volume of our D-edged tetrahedron, where D = the diameter of a CCP sphere.
