Layered double hydroxides are obtained by partial isomorphous substitution of divalent metal ions by trivalent metal ions in the structure of mineral brucite, Mg(OH)(2). The widely reported three-layer polytype of rhombohedral symmetry, designated as polytype 3R(1), is actually a one-layer polytype of monoclinic symmetry (space group C2/m, a = 5.401 angstrom, b = 9.355 angstrom, c = 11.02 angstrom, beta = 98.89 degrees). This structure has a cation-ordered metal hydroxide layer defined by a supercell a = root 3 x a(0); b = 3 x a(0) (a(0) = cell parameter of the cation-disordered rhombohedral cell). Successive layers are translated by (1/3, 0, 1) relative to one another. When successive metal hydroxide layers are translated by (2/3, 0, 1) relative to one another, the resultant crystal, also of monoclinic symmetry, generates a powder pattern corresponding to the polytype hitherto designated as 3R(2). This structure model not only removes all the anomalies intrinsic to the widely accepted cation-disordered structure but also abides by Pauling's rule that forbids trivalent cations from occupying neighboring sites and suggests that it is unnecessary to invoke rhombohedral symmetry when the metal hydroxide layer is cation ordered. These results have profound implications for the correct description of polytypism in this family of layered compounds.