Euler angles for G 2

We provide a simple coordinatization for the group G2, which is analogous to the Euler coordinatization for SU(2). We show how to obtain the general element of the group in a form emphasizing the structure of the fibration of G2 with fiber SO(4) and base H, the variety of quaternionic subalgebras of octonions. In particular this allows us to obtain a simple expression for the Haar measure on G2. Moreover, as a by-product it yields a concrete realization and an Einstein metric for H. © 2005 American Institute of Physics.