K-noids are constant mean curvature (CMC) immersions of a k-punctured Riemann sphere into Euclidean 3-space with ends asymptotic to CMC Delaunay half-cylinders of revolution.
These fournoids were constructed by the loop group Weierstrass representation of CMC surfaces. Unlike k-noids with Platonic symmetries. which are based on trinoids and hence have no accessory parameters in their Weierstrass representations, these surfaces have infinitely many accessory parameters, which were computed by numerical search.
The lines on the surfaces are curvature lines meeting at four umblics,
two of which are visible in each image.
The end axes, while colplanar, are not concurrent.
|
|
|
|
|
|