# Bradford Hansen-Smith

The models I make are explorations into the nature of the folded paper circle as a comprehensive and self-generating form that only requires a systematically folded regular triangular grid. The endless reconfiguring of the circle to this grid of various frequencies and multiple joining can generate an extraordinary number of formal systems as well as revealing unexpected amounts of mathematical information. I have a need to make these models since my imagination is always surprised at the reality of what appears.

Joining twenty regular open tetrahedra in an icosahedron pattern will by nature open the vertices. Attaching the midpoints of all edges between tetrahedra stabilizes the assembly allowing twelve openings between inside and outside. The potential for design possibilities of a primitive life form was of interest. To make this structurally viable and functional the design needed more complexity that would not violate the elements already in place and could be reformed using the same folded grid. The vertex locations have been covered leaving one open to the interior. The inherent structural association to the dodecahedron has been preserved.

In exploring variations of a specific circle reconfiguration using the 16-frequency folded diameter grid, one form had interesting possibilities for an open sphere to show some of the internal structure as well as the external shell. Because of the open nature of the individual unit and by joining twenty of them in an open pentagon relationship the under-layer of structural design become viable, similar to the skeletal form of a simple organism.

Joining two open truncated tetrahedra suggested body segments of an insect. Understanding there are design limitations by the geometry already in place I began to explore this direction of development. The openings suggested internal forming might be pushed through extending to the outside. Various forms are given to the extensions indicating possibilities for different types of functional interacts. One opening is left open for direct exchange between inside and outside. All circles are folded to the same triangular grid using variations from the same reformation.