  In this short note, we prove that the space of all admissible piecewise
linear metrics parameterized by length square on a triangulated manifolds is a
convex cone. We further study Regge's Einstein-Hilbert action and give a much
more reasonable definition of discrete Einstein metric than our former version
in \cite{G}. Finally, we introduce a discrete Ricci flow for three dimensional
triangulated manifolds, which is closely related to the existence of discrete
Einstein metrics.
