## Artists

## Statement

When I fold origami tessellations, I feel like I am reaching out and touching the underlying structures of reality. Folding the single sheet of paper into complex repeating patterns requires intimate knowledge of symmetries: fundamental mathematical truths that are found on so many scales of nature, from the structure of graphene to spiral galaxies. My work represents the joy of discovery and the fascination of controlled complexity. Every feature of the tessellation is planned, from the symmetries to the underlying tiling to the interaction of the pattern with the edge of the paper, but an observer will see only the mystery of many parts that somehow came from a single sheet.

## Artworks

Extracted exemplifies using a broader symmetry structure than the tiling requires. The underlying tiling is a 6.4.3.4 uniform tiling with 60/120 degree rhombi instead of squares, which would typically be filled by one choice of hexagon, one choice of rhombus, and one choice of triangle twist with the global symmetry of each twist matching its maximum local symmetry. By choosing a second hexagon and second rhombus twist, Extracted shows that this is not the only possible application of symmetry to the tiling and that there are many ways to finish the tessellation given a traditional starting point. Additionally, the background grid was customized specifically to this pattern so that the pattern repeats align with the edge of the paper.

Barnacles features hexagon twists enclosed by trapezoids to create a super-hexagon that tessellates the paper - and it's all folded from a single hexagonal sheet of paper! The symmetry positions and twist shapes were determined by the underlying tiling, and the fact that the tiling is 2-colorable guarantees that all right-handed twists will connect to left-handed twists and vice versa. The direct connection of the hexagon to six trapezoids is a feature that I haven't seen elsewhere, but one that gives rise to a variety of interesting tilings.