Catalyzes the reversible reduction of methenyl-H(4)MPT(+) to methylene-H(4)MPT. 5,10-methenyl-5,6,7,8-tetrahydromethanopterin + H2 = 5,10-methylenetetrahydromethanopterin + H(+) Activity requires salt; 100 mM sodium or potassium salts of chloride, phosphate or sulfate are equally effective. Inactivated by O(2). Optimum pH is 6.0-6.5 when making H(2) and 7.5 in the other direction. Optimum temperature is 60 degrees Celsius. One-carbon metabolism; methanogenesis from CO(2); 5,10-methylene-5,6,7,8-tetrahydromethanopterin from 5,10-methenyl-5,6,7,8-tetrahydromethanopterin (hydrogen route): step 1/1. Homotetramer. Belongs to the HMD family.