A high coordination lattice was recently introduced for the simulation of coarse-grained rotational isomeric state (RIS) model chains. This second nearest neighbor diamond (2nnd) lattice is formed by connecting every other site on a tetrahedral lattice. Monte Carlo simulations of polyethylene (PE) melts have recently been performed on the 2nnd lattice by incorporating the intramolecular short range interactions from the RIS model and the long range interactions using a potential derived from an averaging procedure of the Mayer function in the expansion for the second virial coefficient. In the present work, the reverse mapping of specific snapshots from the coarse-grained PE melt back to the fully atomistic representation in continuous space is demonstrated. Reverse mapping is, essentially, determining the location of intermediate backbone atoms that are not represented on the 2nnd lattice but exist on the diamond lattice. In certain situations, the new locations of two intermediate atoms may coincide, leading to an unrealistic local conformation with infinite energy. Although these collapse situations are rare in the case of PE, they still present a problem in finding an energetically acceptable snapshot, which can be further subject to energy minimization in continuous space. These local collapse phenomena can be avoided by taking into consideration the geometry of the underlying tetrahedral lattice during coarse-grained simulations. Consequently, specific snapshots from bulk PE simulations are reverse-mapped and their energy is minimized. The cohesive energy densities of these energy-minimized snapshots are very close to the experimental values reported in the literature.