Barth Sextic
Joint with Silviana Amethyst, A physical sculpture of the Barth Sextic, an algebraic surface of degree six
The sculpture, joint work with Silviana Amethyst, is a 5-axis milled physical model of the Barth Sextic surface. The toolpaths were controlled directly from the algebraic surface to the action of the CNC that carved with a square end mill always at right angles to the surface.
It was exhibited at the JMM 2023 Mathematical Art Exhibition in Boston, where it won the AMS prize for best textile, sculpture, or other media.
A degree-6 algebraic surface can have at most 65 ordinary double points, locations where the surface self-intersects in the simplest possible way. The Barth Sextic, discovered by Wolf Barth in 1996, achieves this maximum. The surface also carries icosahedral symmetry: the 60 rotational symmetries of an icosahedron all map it to itself.