Dear Colin
Thank you for your kind and timely explanation of Octonions. In Jonathan Dickau's post of Aug. 21 just before yours he refered to octonions and in the last paragraph of my answer I asked a couple of questions about that.
Thank you for John Baez' paper on octonions, and your explanation of the figures on page 7. I could not help observing that with the great respect I have for Baez's accomplishments us non-academic physicists were a bit scared of being branded by him as cranks when he was on a campaign to expunge our work from the world :) Luckily he did not even notice my papers!
In his paper Baez refers to Wigner's 1930's interest in octonions. Coincidentally my friend Norman D. Cook reworked an idea of Wigner to build a nuclear structure model based on a Face Centered Cubic FCC . In fact I adopted the FCC in my Beautiful Universe model (over the triangular Kepler packing) thanks to Cook's example. I encouraged Cook to present his work in this fqxi contest. Please have a look at it and his book and simulation software on the same subject published by Springer.
Its a small world, and with all these efforts I hope something good will jell in the world of fundamental physics.
With thanks and best wishes,
Vladimir