Many rock-forming chain and sheet silicate minerals, i.e., pyroxenes, amphiboles, micas, and clay minerals, are built from shared chemical building blocks known as T-O-T modules. Each module consists of two opposing chains of vertex-sharing silica tetrahedra (T), which vertically sandwich a ribbon of edge-sharing metal-oxygen octahedra (O) in a T-O-T configuration. These minerals are both abundant (26 % of the crust) and diverse (~23 % of silicate species) in the lithosphere because T-O-T modules are chemically and structurally versatile over a wide range of chemical and physical conditions. Chemically, T-O-T modules can incorporate a multitude of common crustal elements, e.g., O, Si, Al, Fe, and Mg. Structurally, T-O-T modules can be configured in many ways, as a function of the module width and linkage type. Therefore, these minerals lie at the center of understanding geological processes. However, their diversity leads to the minerals developing complex, three-dimensional crystal structures, which are challenging to communicate to general audiences, students, and geoscientists. Current methods for communicating the crystal structures of minerals are limited to ball-and-stick models and computer visualization software, but both methods have limitations in communicating the relationships between these complex crystal structures. Here, we apply 3D printing, modular mineralogy, and pedagogical theory to communicate mineral structures in an accessible, interactive, and versatile manner. The open-source TotBlocks project consists of 3D-printed, T-O-T interlocking bricks, based on ideal polyhedral representations of T and O modules, which are linked by hexagonal pegs and slots. Using TotBlocks, we explore the relationships between modular minerals within the biopyribole (biotite-pyroxene-amphibole) and palysepiole (palygorskite-sepiolite) series, as well as other layered minerals (brucite, kaolinite-serpentine, and chlorite groups). TotBlocks can be used in geoscience outreach settings to show the relationships between different mineral structures in a fun and interactive manner. As for geoscience education, the T-O-T modules within these minerals can be used to visually derive many mineral properties by first principles, e.g., habit, cleavage angles, and symmetry/polytypism. Distinct crystallographic sites can be highlighted for geoscience research. With respect to pedagogical theory, TotBlocks are physical manipulatives that align well with experiential learning theory and constructionism. In conclusion, the TotBlocks project provides an accessible (open-source models, low overhead printing cost), interactive (physical manipulatives allowing students to construct and manipulate mineral structures), and versatile (applications in geoscience outreach, education, and research) way to communicate the crystal structures of common rock-forming minerals.