I am pleased to announce the availability of Fano.pdf, a 241 page pdf file with the 480 octonion permutations (with Fano planes and multiplication tables). These are organized into “flipped” and “non-flipped” pairs associated with the 240 assigned particles to E8 vertices (sorted by Fano plane index or fPi). For each split real even E8 vertex, the algebra root, weight and height are listed along with the Clifford/Pascal binary and physics rotation coordinates. On each page, the E8 particle number, symbol, and assigned 2D/3D shape are shown along with the (a)nti, (p)Type, (s)pin, (c)olor, (g)eneration bitwise quantum assignments. Also included is the particle experimental mass and lifetime along with my ToE theoretically calculated mass. (30MB)
I believe this is the only comprehensive presentation of all 480 Fano planes with their multiplication tables available.
I am improving and tightening the octonion to E8 to particle symmetry assignments which should inform the particle mass/charge assignment (prediction).
Keep looking at the .CDF .NB or interactive pages – it is always up to date.
I am thinking about how the quaternion trialities within the non-associative algebra of octonions relate to time (and differentiate particles). So it is less about E8 and more about how octonions (linked to E8) affect our 4D reality.
I’ve updated all .CDF, .NB and older .NBP demonstration code with Mathematica v.9
This now includes the completed integration of octonions with E8 & the extended Stadard Model particle assignments. This means the 480 octonions are in fact in a 2:1 cover of E8’s 240 vertices (with their association to Lisi’s particle assignments). This creates the opportunity for a self-dual type of “super symmetry” where all three generations emerge from the octonions.