The mapping of rotational isomeric state (RIS) models for chain molecules onto a high coordination lattice may permit efficient simulations of the self-assembly of block copolymers. Recently the second nearest neighbor diamond (2nnd) lattice was introduced for this purpose, and the RIS model for polyethylene was successfully mapped onto that lattice. Here the mapping procedure is extended to the two examples of poly (A-A-B) with A=CH2, B=O or S in order to ascertain whether the mapping can produce reasonable values for the mean square dipole moment, as well as the mean square end-to-end distance, and also to provide mapped RIS chains for construction of block copolymers. Simulations of single chains of polyoxyethylene (POE) and polythiaethylene have been performed on the 2nnd lattice by incorporating short range interactions through an extended RIS formalism. The overall dimensions of the chains, specifically of POE, are in agreement with the unperturbed dimensions of the classical RIS model. The characteristic ratio of the mean square dipole moments for long POE chains is close to the values reported in experiments and earlier RIS calculations. The ratio of the mean square radius of gyration for cyclic to acyclic POE chains of the same degree of polymerization approaches the long chain limit of 1/2. Simulations of single chains have also been performed in varying solvent environments, by implementing long range interactions via the lattice formulation of the second virial coefficient. As a result of these simulations, the strength of attractive and repulsive long range interactions on the 2nnd lattice can be determined for attaining theta solvent conditions.