Geodesic gridshell with a 6-fold symmetry
Posted: May 23rd, 2010 | Author: John Zerning | Filed under: Hexagonal | Tags: 6-fold, Hexagonal | No Comments »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.
The hexagonal face of a truncated tetrahedron marked on a sphere, with a geodesic triangular pattern.
Gridshell with geodesic triangles having a 6-fold symmetry, supported on columns.
Top view. Note how the areas of the geodesic triangles vary. Being relatively large at the crown where the loads are low and smaller towards the supports where the loads increase.
An aggregate of 3 hexagonal geodesic gridshells. Note the clean geometry along the cross-sections where the truncated domes join.