We present here a library of protein mimetic bicyclic peptides. These nanosized structures exhibit rigid backbones and spatially diversifiable side chains. They present modular amino acids on all three linkages, providing access to a true 3D diversifiable chemical space. These peptides are synthesized through a Cu-catalyzed click reaction and a Ru-catalyzed ring-closing metathesis reaction. Their bicyclic topology can be reduced to a linear one, using Edman degradation and Pd-catalyzed deallylation reactions. The linearization approaches allow de novo sequencing through mass spectrometry methods. We demonstrate the function of a particular peptide that was identified through a high throughput screening against the E-363-R-378 epitope on the intrinsically disordered c-Myc oncoprotein. Intracellular delivery of this peptide could interfere with the c-Myc-mediated transcription and inhibit proliferation in a human glioblastoma cell line.