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Proteins are involved in almost all functions in a living cell, and functions of proteins are realized by their tertiary structures. Obtaining a global perspective of the variety and distribution of protein structures lays a foundation for our understanding of the building principle of protein structures. In light of the rapid accumulation of low-resolution structure data from electron tomography and cryo-electron microscopy, here we map and classify three-dimensional (3D) surface shapes of proteins into a similarity space. Surface shapes of proteins were represented with 3D Zernike descriptors, mathematical moment-based invariants, which have previously been demonstrated effective for biomolecular structure similarity search. In addition to single chains of proteins, we have also analyzed the shape space occupied by protein complexes. From the mapping, we have obtained various new insights into the relationship between shapes, main-chain folds, and complex formation. The unique view obtained from shape mapping opens up new ways to understand design principles, functions, and evolution of proteins., Author summary Proteins are the major molecules involved in almost all cellular processes. In this work, we present a novel mapping of protein shapes that represents the variety and the similarities of 3D shapes of proteins and their assemblies. This mapping provides various novel insights into protein shapes including determinant factors of protein 3D shapes, which enhance our understanding of the design principles of protein shapes. The mapping will also be a valuable resource for artificial protein design as well as references for classifying medium- to low-resolution protein structure images of determined by cryo-electron microscopy and tomography.