Abstract. This paper utilizes geometry and graphics to demonstrate a process of three-dimensional spatial transformation. A transformation defines how structures behave in addition to how they are made. Here, the transformation process is applied to several different frames of reference. Material polyhedra transform into pairs of spatial lattices and the lattices transform into each other; the lattices also transform into twisted loops with exostructural and endostructural modes. The exo/endo interactions transform the hypercube into a pair of twisted loops and the twisted loops become a source for sculpture
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