Rechargeable all-solid-state lithium-ion batteries utilizing a fast lithium superionic conductor electrolyte (SCE) has the potential to revolutionize energy storage by providing an inherently safer, less flammable alternative to traditional organic electrolyte-based batteries.  Synthesized from 70Li₂S:30P₂S₅ glass-ceramic, the Li₇P₃S₁₁ metastable crystal is a promising SCE that exhibits very high ionic conductivity of 17 mS/cm, comparable to those of liquid electrolytes. In this work, we present a combined computational and experimental study on this compound. We find that though Li₇P₃S₁₁ is predicted unstable at zero temperature, it becomes stable at 630 K when vibrational entropy contributions are accounted for, in excellent agreement with experimental measurements. We will also report on the calculated surface energies and Wulff shape of the Li₇P₃S₁₁ crystal. Finally, we demonstrate that ab initio molecular dynamics (AIMD) simulations predict Li₇P₃S₁₁ to have a significantly higher room-temperature ionic conductivity than previously reported, suggesting that there is significant scope for the further optimization of this material.