Golden Diamond Space Enclosing System
Using the Geometry of the Rhombic Triacontahedron
The Rhombic Triacontahedron provides both the diamond shapes (rhombs) and 3-dimensional geometry. used to define this space enclosing system. One distinct advantage of this system is that all rhombs identical. Thus it would simplify manufacturing and reduce material costs.
Since this approach is filled with the Golden proportion (see below) it may also be fundamentally pleasing to the eye. For example, the diagonals of the faces are in the Golden Proportion.
The similarity to this example of Penrose tiling, from the Wikipedia article of the same name, is obvious. (image credit) The 3D version has the advantage of using only a single face, while the 2D Penrose tiling uses two basic types of tiles. Also, because of its zonahedral symmetry the rhombic triacontahedron, by the simple process of extrusion, can add more belts (zones) of golden rhombs at will. This further enhances its design potential.
Diagram of Penrose Tiles from WikipediaWith thin and wide rhombic tiles.
Here are three basic methods for adding tiers to create domes with the Golden Diamond system. All three approaches share the same plan view (upper left). On the upper right is the ‘Star‘ method. In the lower left is the ‘Simple‘ method, while the ‘Full‘ Method in in the lower right.
Credits: Rhombic triacontahedron , Net of same , Dihedral Angle , Facial angles
This slightly more complex Golden Diamond dome uses the ‘Simple’ and the ‘Full’ methods. The bottom two tiers also include the ‘Full+’ method, which contains additional downward facing rhombs. This is simply one example of how different methods may be combined to provide more flexibility and variety than offered by each individual method.
Also, there are additional methods. Consider the edge length as unity (1). For example visualize the ‘Star’ translated down a unit rather than up. Another would be outer lower belt of rhombs in the ‘Full’ method translated up a unit from the current position. There more methods that are still regular and symmetrical in the plan view.
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