Two subdivision methods based on the regular octahedron for single- and double-layer spherical geodesic domes

Abstract

The paper presents the topological–geometric analysis of a selected number of space frames configurations for geodesic domes which are generated from the regular octahedron. Two subdivision methods for spherical triangles, proposed by Fuliński, were used to create two families of structures. The first family consists of six single-layer and six double-layer geodesic domes shaped on the basis of the first method of subdivision, while the second family contains six single-layer and six double-layer geodesic domes shaped on the basis of the second method of subdivision. The calculated results of the geometric parameters of the analyzed structures were used to create original formulas that allow for more advanced structures to be achieved, that is, with a larger number of nodes and struts. The geometric results were also used to create nomograms showing the range of struts of the same length for double-layer geodesic domes. In both single-layer and double-layer domes, the number of groups of struts of equal lengths and the number of faces with different areas are smaller for structures created according to the first method of subdivision. The comparison of the resulting element quantities of two methods shows that the largest differences appear between the domes with a larger number of struts (up to 67%). Here, the analysis might help the designer reach a final decision on the better choice of topology, in particular, when this aspect is combined with other design goals, such as efficiency, economy, utility, and elegance in the design of the structure and the cover of large areas.