Edmund Harriss, Silviana Amethyst
We started working together at the "Illustrating Math" semester at
ICERM, with the goal of exploring toolpaths to make algebraic surfaces
on a CNC mill. On a 5-axis mill, the tool can control both the
position of cut and the direction, thus producing a very high finish
quality with a relatively small number of paths. Our goal was to
create the toolpaths to machine the surface directly from the
mathematical surface, rather than through some sort of proxy, for
example in first creating a mesh, and then applying a more standard
strategy.
The modularity of the Barth Sextic — 20 identical units — makes it
an obvious choice to mill in pieces. As the sextic surface with
the maximum possible number of double-point singularities (here
the positions of the brass rods and the spikes on the outside mark
the real singularities), this structure is mathematically
interesting as well as beautiful. The engagement from the
materials of the structure has already lead to many conversations
with many people about the nature of singularities and algebraic
surfaces.