Space-filling Tetrahedra Surface Configuration Study (Extensible Strut, Flexible Node)
The study started with the investigation of rules which govern equilateral triangles, being the basis for the construction of the faces of regular tetrahedra. A mathematical function was created to explain the relationship between minimum and maximum strut extensibility.
Formulas for manipulating regular tetrahedra were examined next.
Regular Tetrahedra can only fill area along a plane in an interlocking fashion. This image examines the phenomena.
Here are top view and perspective view Rhino renditions of a regular tetrahedra array surface.
Further research uncovered that certain irregular tetrahedra are capable of filling space, and therefore, are suitable for manipulating and constructing surface structures.
The following sequence depicts the folding of a tetrahedra cube net to demonstrate that it is indeed a viable solution to tetrahedra filling space and for being usable in the construction of structured surfaces:
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The structured surface developed from this tetrahedra cube module is illustrated below:
Next Steps:
-Develop a logical/mathematical function to describe the sharing of struts both internally within and externally between tetrahedra cube modules.
-Simulate, define, and then be able to manipulate the degrees of freedom the developable structured surface would demonstrate.
-Study applications (such as structural facade system with varying shape and apetures, etc.).
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