James Mallos
I am interested in simple descriptions of surfaces and shapes. Tensegrity structures are a practical bridge between surface and shape: like mathematical surfaces, they are shape shifters that can take many conformations, but they favor one with minimum energy, eventually settling into a definite shape.
The cube, like most trivalent topological maps on the sphere, has a Hamilton circuit that visits every vertex without retracing edges. By topologically stretching the Hamilton circuit out to become an equator on the sphere, the non-Hamilton edges are revealed as non-crossing chords in two hemispheres. The chords in each hemisphere are arranged like nested parentheses, one proper parenthesis word in each hemisphere, the two words interleaved along the equator in a particular way. Parenthesis words can be built up from local changes, namely insertions of paired open/close parentheses. Similarly, interleaving can be accomplished one local 'shuffle' at a time. The flip book animates one sequence of these mutations that grows into a cube.