G2 shall be my favorite group! Well, for now. For a while. Or maybe for longer. It's the smallest of the exceptional Lie groups. Found 1893 by Élie Cartan. It was he who suggested to think about it in terms of rolling balls. https://en.wikipedia.org/wiki/G2_%28mathematics%29
Picture two spheres, one three times larger than the other. Imagine them rolling on another without slipping nor twisting. Rolling surfaces have their own branch of mathematics: contact geometry!
This spinor rolling on a projective plane, where the latter has three times the spinor's radius, models the real valued lie algebra g2. However, this also works for complex values. This is what Cartan originally described.