We present previously unreported crystalline and polycrystalline structures for methane hydrates obtained at relatively low pressures. These structures, which contain unusual cages with 12 pentagonal faces and 3 hexagonal faces, were observed during the atomistic simulations of the crystal growth of sI and sII methane hydrates. These 51263 cages have a significant impact on the structure of the resulting crystal and could explain several experimental observations regarding in-situ transformations between sI and sII hydrates. We document a previously unidentified structure of methane hydrates which we designate structure sK. Additionally, we predict a polycrystalline structure consisting of this new hydrate and sI and suggest a mechanism for the formation of a polycrystalline structure consisting of sequences of sI and sII hydrates.