Let us now consider the (possibly an effective) Higgs hypothesis. Since it need not resemble the spin $1/2$ and spin $1$ braids, this one extra state could arise as a three dimensional state formed by symmetrizing the unused tetractys diagonal,
$XXX \oplus YYY \oplus ZZZ$
for some ill defined $\oplus$. Recall that the $XXX$, $YYY$ and $ZZZ$ paths define the axes of the Koide space. Since planes in this space are the basis of triality, we could draw this product as a trivalent vertex with an $H$ at the centre point. This vertex closes the doubled tetractys into a tetrahedron, now with $56 = 2 \times 28$ labels.
Note that Tony Smith's original 1993 calculation of the (so called) truth quark mass, based on triality, gave an estimate of $130$ GeV, not far from the observed value.
6 years ago