High-resolution transmission electron microscope (TEM) images confirm that greenalite and caryopilite are modulated 1:1 phyllosilicates. The octahedrally coordinated Fe (greenalite) and Mn (caryopilite) form trioctahedral sheets. Six-member rings of tetrahedra link to form triangular islands four or five tetrahedra across, with each island coordinating to one octahedral sheet. Adjacent islands are inverted and link to the neighboring octahedral sheet, which results in a triply-intersecting corrugation for the tetrahedral sheet. Islands vary in numbers of tetrahedra about a mean dictated by the octahedral sheet dimension. Island separations range about a mean distance within the X-Y plane, with island alignment fluctuating as a function of lattice vectors defined by the octahedral sheet. The tetrahedra thus show limited short-range order (spanning to five octahedra), but long-range disorder. Linkages of tetrahedra between islands are apparently completely disordered. Because of this disorder, there is no definable unit-cell. Fourier calculations involving non-repeating structures cannot use unit-cell fractional coordinates and Miller indices. We calculated diffraction patterns by finding the real-space coordinates of every atom in the model relative to a defined origin. The reciprocal space variable, d (super *) , is sampled at intervals of 0.005 Aa to build the continuous Fourier transform of the model. Discrete polytypes of 1T and 1M for greenalite and caryopilite, respectively, were identified. Where grains contain mixtures, the relative abundance of each polytype is related to composition, with the dominant polytype based on minimizing misfit between the sheets of octahedra and of tetrahedra. Stacking in greenalite and caryopilite is defined by the relative positions of adjacent octahedral sheets and, therefore, limits on the displacements of neighboring domains of silicate rings within (001) are possible. Domain boundary linkages, however, cannot be determined precisely by using either diffraction or imaging data.