Affine Root Systems

Affine Dynkin diagrams (from Onischik and Vinberg, Lie Groups and Algebraic Groups)

Kac diagrams of involutions of simple Lie algebras.
These classify the real forms of simple complex Lie algebras. From Onischik and Vinberg. See Strong real forms and the Kac classification.

Kac Diagram type I (type I: equal rank inner class, not Hermitian symmetric)

Kac Diagram type I-II (type II: Hermitian symmetric)

Kac Diagram type II-III (type III: unequal rank inner class)

Rank 2 affine hyperplane diagrams from John Stembridge

A2  B2  G2

Rank 3 ordinary root hyperplanes also from John Stembridge

A3  B3