The optimal solution for the enclosure of space is the geodesic dome with a 5-fold icosahedral symmetry. (The most beautiful molecule, carbon-60, “Bucky ball”, has a 5-fold symmetry).
However, truncated geodesic domes with a pentagonal symmetry are difficult to aggregate in two directions, since the geometry along the cross-sections, where the truncated geodesic domes join together, are messy. This problem can be neatly solved in designing domes with a 6-fold symmetry.
The drawings show a geodesic gridshell with a 6-fold hexagonal symmetry. It is derived by projecting the hexagonal face of a truncated tetrahedron, with a triangular subdivision, on a circumsphere. All the lines follow great circle arcs.