Materials with the crystal structure of γ-brass type (Cu5Zn8 type) are typical representatives of intermetallic compounds. From the electronic point of view, they are often interpreted using the valence electron concentration approach of Hume-Rothery, developed previously for transition metals. The γ-brass-type phases of the main-group elements are rather rare. The intermetallic compound Be21Pt5, a new member of this family, was synthesized, and its crystal structure, chemical bonding, and physical properties were characterized. Be21Pt5 crystallizes in the cubic space group F4̅3m with lattice parameter a = 15.90417(3) Å and 416 atoms per unit cell. From the crystallographic point of view, the binary substance represents a special family of intermetallic compounds called complex metallic alloys (CMA). The crystal structure was solved by a combination of synchrotron and neutron powder diffraction data. Besides the large difference in the scattering power of the components, the structure solution was hampered by the systematic presence of very weak reflections mimicking wrong symmetry. The structural motif of Be21Pt5 is described as a 2 × 2 × 2 superstructure of the γ-brass structure (Cu5Zn8 type) or 6 × 6 × 6 superstructure of the simple bcc structural pattern with distinct distribution of defects. The main building elements of the crystal structure are four types of nested polyhedral units (clusters) with the compositions Be22Pt4 and Be20Pt6. Each cluster contains four shells (4 + 4 + 6 + 12 atoms). Clusters with different compositions reveal various occupation of the shells by platinum and beryllium. Polyhedral nested units with the same composition differ by the distance of the shell atoms to the cluster center. Analysis of chemical bonding was made applying the electron localizability approach, a quantum chemical technique operating in real space that is proven to be especially efficient for intermetallic compounds. Evaluations of the calculated electron density and electron localizability indicator (ELI-D) revealed multicenter bonding, being in accordance with the low valence electron count per atom in Be21Pt5. A new type of atomic interactions in intermetallic compounds, cluster bonds involving 8 or even 14 atoms, is found in the clusters with shorter distances between the shell atoms and the cluster centers. In the remaining clusters, four- and five-center bonds characterize the atomic interactions. Multicluster interactions within the polyhedral nested units and three-center polar intercluster bonds result in a three-dimensional framework resembling the structural pattern of NaCl. Be21Pt5 is a diamagnetic metal and one of rather rare CMA compounds revealing superconductivity (Tc = 2.06 K).