The crystal structure of cumengéite, Pb21Cu20Cl42(OH)40, tetragonal, a= 15.065(2), c= 24.436(5) Å, V = 5546(2) Å3, space group I4/mmm, Z = 2, has been solved by direct methods and refined by least-squares to an R index of 7.1 % for 1158 observed (I > 2.5σ I) reflections. The cumengéite structure shows a very diverse range of cation coordinations. There are five distinct Pb sites with the following coordination polyhedra: octahedron, square antiprism, augmented trigonal prism, a very distorted biaugmented trigonal prism and a fairly regular biaugmented trigonal prism, the latter being only half-occupied; there are two distinct Cu sites with octahedral and square pyramidal coordination respectively. The coordination polyhedra share elements to form prominent columns or rods of polyhedra parallel to the c-axis and centred on the 4-fold axes of the unit cell. These rods form a body-centred array, and link by sharing elements of their coordination polyhedra.

The crystal chemistry of rhodizite was re-examined using data from high-resolution electron microscopy (HREM), magic angle spinning nuclear magnetic resonance (MASNMR), a single crystal X-ray structure refinement, and a new chemical analysis. The analysis calculates to the formula: (K0.46Cs0.36Rb0.06 Na0.02)Σ0.90Al3.99Be4(B11·35Be0.55Li0.02)O28· The distribution of alkali cations was shown to be truly random by HREM images and computer image simulations. The distribution of boron and beryllium was monitored by MASNMR, the spectra for both elements gave only single resonances indicating that all beryllium and boron atoms are located in chemically equivalent sites. The structure of rhodizite was refined by single crystal X-ray diffraction techniques. The mineral is cubic a = 7.318(1) Å, space group P3m. A full matrix least-squares refinement using 152 unique observed reflections [F > 3σ(F)] converged to R = 0.0344. The refinement confirmed the basic structure as determined by Taxer and Buerger (1967), 4 beryllium atoms of the unit cell were found to occupy a 4e special position, the remaining 0.5 being randomly distributed with the 11.35 boron atoms over the 12h sites.