  The action of the symmetric group of degree 4 on the Tetrahedron algebra,
introduced by Hartwig and Terwilliger, is studied. This action gives a grading
of the algebra which is related to its decomposition into a direct sum of three
subalgebras isomorphic to the Onsager algebra. The ideals of both the
Tetrahedron algebra and the Onsager algebra are determined.
