Abstract: A composite wall structure for use in a building, such as a geodesic dome, or the outer hull of a pressurized vehicle, such as an airship or submarine, is formed by interconnecting a plurality of three dimensional triangular shaped cells into a shape of desired contour, such as planar or curved, with each individual cell having a sealed chamber that is pressurized, and securing a fluid impervious closure skin to the connected array of cells. Each cell is formed by connecting planar rectangular sidewalls into a triangular frame having opposite sides and attaching a planar triangular panel to each side of the frame in a manner to form a pressure sealed chamber. The hull structure of predetermined shape is capable of captivating a volume of air and/or resisting buckling or failure resulting from fluid pressure on the hull during operation in air or water environments.

Abstract: A geodesic dome is created by the steps of: (a) generating a mathematical model of a geodesic dome, (b) fabricating components with which to form a geodesic dome according to the model; and (c) fastening the components to each other according to the model. In the model, M base triangles are generated in a closed three-dimensional shape. M is at, least four, with eight being preferred and the preferred closed three-dimensional shape being a regular octahedron. The closed three-dimensional shape has a center point from which each vertex of each of the base triangles is equidistant, this distance being a geodesic radius. Each leg of each base triangle is then subdivided into N segments of equal length, N being at least two, with eight being preferred, thus defining N+1 segment endpoints or intersections along each leg. A line is then generated between each intersection and two corresponding intersections, thus defining N2 smaller triangles per base triangle.