A method and apparatus for geodesic sphere construction provides a construction framework from an extrusion system that, when fabricated, generates the geometries of the geodesic sphere or dome, and also is configured to interlock with the triangular exterior panels to form a waterproof system. The apparatus includes an extruded strut portion having a cross-section, and a vertex component having the same cross-section, with a sliding connector portion adapted to slide into and join the strut portion and vertex component to form the geodesic frame work of a geodesic strut and panel system. The extruded strut and vertex components have a centerline bearing opposing dihedral angles. The vertex connectors are each set at the appropriate face angle and axial angle according to their location on the geodesic structure. Thus, the vertex component generates both the surface angles on a geodesic sphere and the axial angles which produce the curvature of the geodesic dome.