A two-dimensional structural model of polymeric methyltrioxorhenium (MTO) has been established by means of diffraction techniques and a variety of analytical methods. The unusual compound, constituting the first example of a polymeric organometallic oxide, has a layer structure of methyl-deficient, comer-sharing ReO5(CH3) octahedra. It adopts the three-dimensional extended ReO3 motif in two dimensions as a {ReO2}infinity network. Adjacent layers of corner-sharing ReO5(CH3) octahedra (A) are capable of forming staggered double layers (AA’). In the crystalline areas of "poly-MTO", such double layers are separated by intercalated water molecules (monolayer) (B) with an ...AA’BAA’... layer sequence. For the partially amorphous areas of "poly-MTO", we propose a turbostratic and 00l-defect stacking model for the "poly-MTO" and water layers. Interactions between the adjacent layers in this polymeric MTO are very weak, resulting in graphite-like macroscopic properties such as flaky appearance, softness, and lubricity. High electric conductivity results from understoichiometry with respect to the CH3/Re ratio (9.2/10) and partial reduction by extra hydrogen equivalents. For the purpose of comparison, the solid-state structure of "monomeric" MTO as established by a combination of X-ray and powder neutron diffraction techniques is also reported.