A promising route to protein-mimetic materials capable of complex functions, such as molecular recognition and catalysis, is provided by sequence-defined peptoid polymers, structural relatives of polypeptides. Peptoids, which are relatively non-toxic and resistant to degradation, can fold into defined structures through a combination of sequence-dependent interactions. However, the range of possible structures accessible to peptoids and other biomimetics is unknown, and our ability to design hierarchical protein-like architectures from these polymer classes is limited. I will describe our use of molecular dynamics simulations, together with scattering and microscopy data, to determine the atomic-resolution structure of the recently-discovered peptoid nanosheet, an ordered supramolecular assembly that extends macroscopically in only two dimensions. Our simulations show that nanosheets are structurally and dynamically heterogeneous, can be formed only from peptoids of certain lengths, and are potentially water- and ion-porous. Moreover, their formation is enabled by peptoids’ adoption of a secondary structure not seen in the natural world. This structure, a zig-zag pattern that we call a Sigma-strand, results from the ability of adjacent backbone monomers to adopt opposed rotational states, thereby allowing the backbone to remain linear and untwisted. Such a binary rotational state motif is not seen in protein regular structures, which are built generally from one type of rotational state. Linear backbones tiled in a brick-like way form an extended two-dimensional nanostructure.