Hodograph equations in relativistic gas-dynamics admitting an infinite number of symmetries

A straightforward application of the Lie-group theory to the linear equation, which describes the relativistic one-dimensional flow in the hodograph plane, is carried out. It is shown that, for particular equations of state, one has an infinite number of symmetries. In this case, transformations can be found that reduce the hodograph equation to a form directly integrable. The remarkable aspect of the analysis is that one of these equations of state is identified as that characterizing a one-dimensional fully degenerate Fermi gas. Astrophysicists might find this result useful in practical applications.