Polymer electrolytes—salts (such as LiCF3SO3) dissolved in solid, high-molar-mass polymers (for example, poly(ethylene oxide), PEO)1,2,3—hold the key to the development of all-solid-state rechargeable lithium batteries4. They also represent an unusual class of coordination compounds in the solid state5. Conductivities of up to 10−4 S cm−1 may be obtained, but higher levels are needed for applications in batteries5,6,7. To achieve such levels requires a better understanding of the conduction mechanism, and crucial to this is a knowledge of polymer-electrolyte structure. Crystalline forms of polymer electrolytes are obtained at only a few discrete compositions. The structures of 3 : 1 and 4 : 1 complexes (denoting the ratio of ether oxygens to cations) have been determined5,8,9. But the 6 : 1 complex is of greater interest as the conductivity of polymer electrolytes increases significantly on raising the polymer content from 3 : 1 to 6 : 1 (refs 10, 11). Furthermore, many highly conducting polymer-electrolyte systems form crystalline 6 : 1 complexes whereas those with lower conductivities do not. Here we report the structure of the PEO:LiAsF6 complex with a 6 : 1 composition. Determination of the structure was carried out abinitio by employing a method for flexible molecular structures, involving full profile fitting to the X-ray powder diffraction data by simulated annealing12. Whereas in the 3 : 1 complexes the polymer chains form helices, those in the 6 : 1 complex form double non-helical chains which interlock to form a cylinder. The lithium ions reside inside these cylinders and, in contrast to other complexes, are not coordinated by the anions.