Duston Wetzel, PhD

Statement

I have tinkered with stable arrangements of woven helices since 2019. My initial inspiration was to model the approximately helical geodesics of Alan Schoen’s gyroid. I have also been influenced by the work of Alexandru Usineviciu, Paul Gailiunas, Moses Gaither-Ganim, William Holt, Wenjie Zhou, Alison Martin, Jens Kieselstein, and Kiju Kang. My method involves winding wire around a rod and stretching the resulting helix to the correct pitch, cutting it into segments, and winding them into place in a larger structure, making stable "crossings" of two to six helices as I go. I have assembled twenty-three unique triply periodic helical weaves and here I display five of the newest. I also display one novel tetrahedral model with bent helices.

Artworks

Here I present five novel models of triply periodic helical weaves. One is the <111> expanded octahedral weave discovered by Paul Gailiunas for our 2024 paper. One is another omega weave with quartet crossings. Two have stacked offset layers of parallel helices, one square and one hexagonal. One is stacked flat rhombic crossings simply repeated with the same orientation. These represent new ways of making 3D materials out of a 1D medium.

Here is a helical weave with bent axes. The axes of the helices themselves form partial larger helices. I call this a helical helical weave. In this example, the overall form resembles the center of a <110> Borromean tetrahedron, a helical weave Alexandru Usineviciu and I collaborated on in 2024.