umbilic torus ring - the umblic torus is a three dimensional form with one side and one edge much like a mobius loop except with one less edge. it can be easily described as a looped triangular extrusion with a one third twist.
model made in solidworks 09

umbilic torus ring - once the initial form is built a guide curve is traced on the side of the form and a profile can be swept.
models made in solidworks 09
rendered in hypershot

ring - models made in solidworks 09

umbilic torus ring - to build the form I started with 8 profiles to exactly control the edge as it moves around itself. Because the form is self intersecting a typical sweep was not possible. to solve for this i had to individually create curvature continuous surfaces in each section of the wire frame model then knit the surfaces together.
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