Transmission electron microscopy to investigate the crystallography of Hg5In2Te8 precipitation in single crystals of Hg3In2Te6. Both the matrix and precipitate phases were confirmed to have the F(-)43m space group. The lattice constant of the precipitates was measured to be a = 1.27 nm, which is approximately double that of the matrix (0.63 nm). Three crystallographically equivalent variants of the precipitate phase were observed to exhibit a cylindrical morphology, dispersed uniformly throughout the matrix. The preferred growth direction of all three variants was along < 001 >(m). The crystallographic orientation relationship (OR) between the precipitates and matrix was found to be a cubic parallel OR. High resolution imaging indicated that the precipitate-matrix interface was fully coherent. The precipitate crystals were found to correspond to the lowest sigma value of the near coincidence site lattices when performing a 0 degrees or 90 degrees mutual rotation. Finally, the existence of Hg5In2Te8 precipitation was found to have a negative effect on the optical properties according to the infrared transmittance measurement. The results in this paper may have a guiding significance on the relationship between the precipitate and optical properties of similar materials.