Symmetries of the Eikonal equation

•The symmetry Lie algebra of the Eikonal Equation is being found.•The Optimal system of the Lie algebra is being classified.•Invariant solutions have been found. 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.