Symmetries of the Eikonal equation

The infinitesimal algebra of Lie symmetries of the Eikonal equation is shown to be isomorphic to o(n+1,2) when there are n independent variables. An explicit basis is found that is aligned with the standard basis coming from the standard matrix representation of o(n+1,2) thereby making it possible to read off inequivalent one-dimensional symmetry vector fields. The symmetries are used to construct various solutions of the Eikonal equation.