k-noid

In differential geometry, a k-noid is a minimal surface with k catenoid openings.

The first k-noid minimal surfaces were described by Jorge and Meeks in 1983.

[1] The term k-noid and trinoid is also sometimes used for constant mean curvature surfaces, especially branched versions of the unduloid ("triunduloids").

[2] k-noids are topologically equivalent to k-punctured spheres (spheres with k points removed).

k-noids with symmetric openings can be generated using the Weierstrass–Enneper parameterization

[3] This produces the explicit formula where