Barth Sextic
A physical sculpture of the Barth Sextic — an algebraic surface of degree six with the maximum possible number of ordinary double points (65). Winner of 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. Finding a surface that exactly meets a theoretical upper bound is rare in algebraic geometry; the Barth Sextic is one of those exceptional objects.
The surface also carries icosahedral symmetry: the 60 rotational symmetries of an icosahedron all map it to itself. This hidden connection between an extremal algebraic surface and one of the five Platonic solids is part of what makes the geometry so striking.
The sculpture is a 3D-printed physical model of the surface, chosen specifically to make the nodes and the overall form tangible at a human scale. It was exhibited at the JMM 2023 Art Exhibit in Boston, where it won the AMS prize for best textile, sculpture, or other media.
