Given the E8 Cartan matrix (above) and a Dynkin diagram node ordering of:One choice of simple roots is given by the rows of the following matrix:: formula_8===Weyl group===The Weyl group of E8 is of order 696729600, and can be described as O(2): it is of the form 2.
One choice of simple roots for E8 (by no means unique) is given by the rows of the following matrix:: formula_18=== E8 root lattice ===The integral span of the E8 root system forms a lattice in R8 naturally called the E8 root lattice.