F4 is the name of a Lie group (and also its Lie algebra). It is one of the exceptional simple Lie groups.

Table of contents
1 Roots of F4
2 Weyl/Coxeter group
3 Cartan matrix

Roots of F4

Simple roots

Weyl/Coxeter group

Its Weyl/Coxeter group is the symmetry group of the 24-cell.

Cartan matrix

See also Simple Lie group, Lie group, Weyl group, Dynkin diagram.