Fuller domes or geodesic domes are partial-spherical shell structures composed of discrete bars that follow a triangular pattern. The layout of the pattern is derived from the projection of a Platonic solid (most often a icosahedron, a regular convex polyhedron with 20 equilateral triangular faces) inscribed into a sphere onto its surface. Fuller domes are very material-efficient structures; they are extremely light and strong. In his patent on a framework for enclosing space, Richard Buckminster Fuller claims that the three-way grid layout of a Fuller dome, where all bars have approximately the same length, leads to almost uniform stressing of all members. This would imply that a Fuller dome is a fully stressed design. Under certain conditions, a fully stressed design is indeed optimal in terms of material use. In this project, the concept of Fuller domes will be extended to what we call Fuller shells: shells with different shapes (such as cones and hyperboloids) that are triangulated according to the same principles as a Fuller dome, also starting from special polyhedra. It will also be investigated how multiple Fuller shells can be connected to form a larger structure. This will lead to an interesting extension of the existing vocabulary for the design of shell structures. The structural behavior of these Fuller shells (the original Fuller dome, the new Fuller shells, and the combined structures) will be investigated using modern analysis techniques, such as the finite element method, and compared with the techniques used by Fuller in the 1950s. This will give insight in the structural behavior of Fuller domes and shells, and it will help to find out if they are indeed structurally superior to other geometries.