The exquisite structure-function correlations observed in filamentous protein assemblies provide a paradigm for the design of synthetic peptide-based nanomaterials. However, the plasticity of quaternary structure in sequence-space and the lability of helical symmetry present significant challenges to the de novo design and structural analysis of such filaments. Here, we describe a rational approach to design self-assembling peptide nanotubes based on controlling lateral interactions between protofilaments having an unusual cross-α supramolecular architecture. Near-atomic resolution cryo-EM structural analysis of seven designed nanotubes provides insight into the designability of interfaces within these synthetic peptide assemblies and identifies a non-native structural interaction based on a pair of arginine residues. This arginine clasp motif can robustly mediate cohesive interactions between protofilaments within the cross-α nanotubes. The structure of the resultant assemblies can be controlled through the sequence and length of the peptide subunits, which generates synthetic peptide filaments of similar dimensions to flagella and pili.