All topological bands of all nonmagnetic stoichiometric materials.

Topological quantum chemistry and symmetry-based indicators have facilitated large-scale searches for materials with topological properties at the Fermi energy (EF). We report the implementation of a publicly accessible catalog of stable and fragile topology in all of the bands both at and away from EF in the 96,196 processable entries in the Inorganic Crystal Structure Database. Our calculations, which represent the completion of the symmetry-indicated band topology of known nonmagnetic materials, have enabled the discovery of repeat-topological and supertopological materials, including rhombohedral bismuth and Bi2Mg3. We find that 52.65% of all materials are topological at EF, roughly two-thirds of bands across all materials exhibit symmetry-indicated stable topology, and 87.99% of all materials contain at least one stable or fragile topological band.