M Theory Lesson 14
The top face really looks like
if we use trees to label choices of bracketings. Carl Brannen's idempotents for lepton masses are also labelled by the parity cube, which describes three directions in space as well as three generations. It is nice to know that this agrees with the number of quark generations that we get by calculating an Euler characteristic for a gluon orbifold modelled by twistors.