Malachite has a layered structure composed of triangular CO3 groups and CuO2(OH)2 coordination squares of two types. In 2D projection, each layer can be decomposed into two OD strips: the A strip, containing CO3 groups and square co-ordinations of Cu2, with idealized symmetry pgm2, and the B strip, without CO3 groups, with symmetry p2 (the b axis of malachite is the infinite strip direction). In the 3D structure, these strips form the ‘A' OD-layers with symmetry reduced by coordination requirements to approximately p2212, which alternate with the ‘B' OD-layers with layer symmetry . The B-layer can assume two positions, which are related by a 180° rotation axis running through the C1 and O1 atoms of the CO3 group in the A-layer. This axis is oriented close to *. The fit of the A-layer and of the coplanar rotated B-layer is hindered by the presence of important partial gaps and overlaps at the boundary. Inclining these two structure portions towards one another, together with small positional adjustments, appears to alleviate the misfit problems; the two layer portions so related form an angle of about 124°, i.e., they form a twin relationship. This desymmetrization of the malachite structure away from the ideal model results in occasional twinning instead of the fully developed monoclinic polytype structure which is derived in this paper. In the structure of the Cu-Zn analogue, rosasite, the above-described match problem is solved in a different way, by shifting a Zn coordination octahedron (which replaces Cu2 in malachite) into the interlayer space. Malachite polytypes 1 and 2 and rosasite illustrate three different orientations of P21/a symmetry elements with respect to the structural layers, resulting in three different structure configurations.