Contents

# Contents

## Idea

(graphics grabbed from Wikipedia here)

This manifests itself in “triality” symmetries enjoyed by the objects that are labled by D4 in an ADE-classification.

Specifically for the simple Lie group SO(8) corresponding to D4, triality is the statement that the two spin representations of the corresponding spin group $Spin(8)$ and the defining vector representations are all isomorphic, and in a nice way.