[n]Diamondoids are hydrocarbons whose carbon skeleton is a portion of the diamond lattice, and contains n adamantane cells (or units) sharing chair-shaped hexagons of carbon atoms. When centers of these adamantane units are connected by lines, the resulting construction is called the dualist of the diamondoid, and it also is similar to a portion of the diamond lattice. While these hydrocarbons can be distinguished by the Balaban-Schleyer nomenclature system, substituted derivatives are to be described by the IUPAC von Baeyer nomenclature that attributes a unique number (locant) to each carbon atom within a molecule. In this paper, von Baeyer names and corresponding atom numberings were obtained by the computer program POLCYC for members of two classes of diamondoids: [n]catamantanes whose dualists are tight helices, and [n]perimantanes whose dualists are all-trans-perhydroacenes; general numbering schemes were derived for these compound classes. The structures and some regularities in their structural properties are discussed.