# Jonathan Leavitt

When I went to college, I had to decide whether to major in art or mathematics. I ended up pursuing ceramic sculpture and left math studies behind. Years later, when I had my own studio, independent from schooling, I wanted to find a craft that was uniquely my own. I had a fascination with fractals, making paper cut-outs("snowflakes"), and exploring polyhedron ideas on graph paper. All these elements came together in now, a fusion of art and mathematics, when I decided to try placing 2-d images onto the 3-d forms of polyhedrons. Matching the symmetries of the 2-d designs to the symmetries of the polyhedron faces became my fascination, as the results seem to vibrate with a new form of beauty unlike anything I had seen previously.

This piece exemplifies the process I called "styration". It is, in fact, a "2nd generation styrated tetrahedron". Years ago, I had a fascination with envisioning 3-d fractals. After having made so many polyhedrons, it was only natural that I would try constructions in that direction. I was familiar with Koch fractals for many years, so I was pleased to come upon this new process. Even though the process has been applied only 2 times here, the result is quite complex. With its 168 faces and so many indentations, it was a new challenge, indeed, to construct. The continuous paper cut-out pattern applied to its surface required several different folding patterns to accommodate so many different face shapes.

Take a cube and tetrahedron of equal volume and nest them together about a shared center so that 4 of the corners of the cube symmetrically extend out through the middle of each of the tetrahedron's triangular faces. Then, connect the centers of this polyhedron's adjacent faces to create new edges that slice or extend across the middle third of the polyhedron's edges ( a process I call "styration") to generate my polyhedron. The cube section is decorated with a paper cut-out pattern that matches across the edges. The tetrahedron section has an M-set fractal pattern on its surfaces. The turquoise color set against the purple also aids in the balance between the two sections. The cube and the tetrahedron have a fresh new juxtaposition here.

This 242-sided polyhedron demonstrates a process I call "gemming", repeated 4 times to the dodecahedron. Gemming involves slicing off the corners to form new faces, so that the new vertices lie on the midpoints of the original edges. Gemming multiple times has the effect of rounding the original form. Doing it infinitely would yield a smooth surface. This piece has rectangles, trapezoids, rhombuses, and triangles around the original pentagons, as its faces. I used a fractional exponent Mandelbrot set fractal with added symmetries to decorate the faces so that the pattern is continuous across the edges, forming a unified whole. Then, I placed a unique paper cut-out over each pentagonal face, to bring more visual diversity around its form.