Cobalt hydroxide and cobalt oxyhydroxide derive their crystal structure from brucite mineral. Cobalt hydroxide crystallizes in hexagonal 1H polytype while cobalt oxyhydroxide in rhombohedral symmetry. In spite of the isostructural relationship between cobalt hydroxide and oxyhydroxide, we observe different symmetries. Hexagonal and rhombohedral polytypes are related to each other by a simple translation vector. Translation of AC layers by (1/3, 2/3, 1) and (2/3, 1/3, 1) with respect to each other generates the 3R polytype. Careful evaluation of the X-ray powder diffraction (PXRD) patterns of cobalt oxyhydroxide reveals the exact stacking sequence to be AC CB BA. The structural transformation of cobalt hydroxide to cobalt oxyhydroxide is reported.