Involved in the hydrolysis of the beta-gamma-phosphoanhydride linkage of triphosphate-containing substrates (inorganic or nucleoside-linked). Catalyzes the hydrolysis of inorganic triphosphate (PPPi), which could be cytotoxic because of its high affinity for calcium ion, thereby interfering with calcium signaling (By similarity). H2O + triphosphate = diphosphate + phosphate