The crystal structures of the beta and gamma polymorphs of Sr3WO6 and the gamma <->beta phase transition have been investigated using electron diffraction, synchrotron X-ray powder diffraction, and neutron powder diffraction. The gamma-Sr3WO6 polymorph is stable above T-c approximate to 470 K and adopts a monoclinically distorted double perovskite A(2)BB'O-6= Sr2SrWO6 structure (space group Cc, a = 10.2363(1)angstrom, b= 17.9007(1)angstrom, c= 11.9717(1)angstrom, beta=125.585(1)degrees at T= 1373 K, Z=12, corresponding to a = a(p)+1/2b(p) - 1/2c(p), b =3/2b(p) + 3/2c(p), c =-b(p) + c(p), a(p),b(p), c(p), lattice vectors of the parent Fm (3) over barm double perovskite structure). Upon cooling it undergoes a continuous phase transition into the triclinically distorted beta-Sr3WO6 phase (space group Cl, a = 10.09497(3)angstrom, b = 17.64748(5)angstrom, c = 11.81400(3)angstrom, alpha = 89.5470(2)degrees, beta= 125.4529(2)degrees, gamma =90.2889(2)degrees at T= 300 K). Both crystal structures of Sr3WO6 belong to a family of double perovskites with broken corner sharing connectivity of the octahedral framework. A remarkable feature of the gamma-Sr3WO6 structure is a non-cooperative rotation of the WO6 octahedra. One third of the WO6 octahedra are rotated by 45 about either the bp or the cp axis of the parent double perovskite structure. As a result, the WO6 octahedra do not share corners but instead share edges with the coordination polyhedra of the Sr cations at the B positions increasing their coordination number from 6 to 7 or 8. The crystal structure of the beta-phase is very close to the structure of the gamma-phase; decreasing symmetry upon the gamma ->beta transformation occurs because of unequal octahedral rotation angles about the bp and cp axes and increasing distortions of the WO6 octahedra.