so if my current guess is right, then the g2 "point" grassmanian is the configuration space of "a fermionic ball rolling on a projective plane of 3 times the radius". the 6 configurations in the main apartment have the ball stationed at one of the 3 "cardinal poles" (the "north-south" pole, the "east-west" pole, and the "front-back" pole", with either of 2 orientations that are 360 degrees apart.