Crystals of Co 3(AsO 4) 2 were grown from the melt of a mixture of Co 2As 2O 7 and As 2O 5. The crystals are isostructural with Mg 3(AsO 4) 2 and are tetragonal with a = 6.858(2), c = 18.872(5) Å, Z = 6, and space group I overline42d . A total of 1048 independent reflections were measured by diffractometer and used in the full-matrix refinement to a final R value of 0.069. The structure contains two distinct AsO 4 groups. Two of the cobalt ions are octahedrally coordinated and a third occupies a overline4 site with four short and four long CoO distances. The crystal structure of Co 3 (AsO 4) 2 is not based on the continuous three-dimensional closest packing of oxygen atoms. Nevertheless the number of oxygen atoms per cubic centimeter is 5.4 × 10 22, which falls in the range of values for hexagonal and cubic closest packed structures. A better measure of the degree to which closest packing is achieved by a structure is suggested. It is based on an analysis of the polyhedra of oxygen atoms which surround each of the oxygen atoms in a structure and their relation to the polyhedra in ideally closest packed structures. In order to facilitate the analysis, polytopes of 11- and 12-vertex polyhedra were studied. A new decahexahedral 11-vertex polyhedron was found.