Background The fast growing Protein Data Bank contains the three-dimensional description of more than 45000 protein- and nucleic-acid structures today. The large majority of the data in the PDB are measured by X-ray crystallography by thousands of researchers in millions of work-hours. Unfortunately, lots of structural errors, bad labels, missing atoms, falsely identified chains and groups make dificult the automated processing of this treasury of structural biological data. Results After we performed a rigorous re-structuring of the whole PDB on graph-theoretical basis, we created the RS-PDB (Rich-Structure PDB) database. Using this cleaned and repaired database, we defined simplicial complexes on the heavy-atoms of the PDB, and analyzed the tetrahedra for geometric properties. Conclusion We have found surprisingly characteristic differences between simplices with atomic vertices of different types, and between the atomic neighborhoods – described also by simplices – of different ligand atoms in proteins.