In a coarse-grained sense both carbon tetrafluoride and neopentane are regular tetrahedral molecules. In an attempt to devise 4 center Lennard-Jones potential models for both substances, it turned out that the reduced side lengths of the tetrahedra L=l/ó are precisely identical, where ó is the site-site potential zero. This implies a conformal interaction model and suggests that the theorem of corresponding states holds precisely. Large scale Monte Carlo simulations have been conducted to set up an equation of state (EOS) for this conformal model over the entire fluid range. Comparison with experiments suggests that this EOS exhibits technical accuracy for both substances.