Platonic noids

Constant mean curvature surfaces in euclidean 3-space

Noids with platonic symmetries [1,2].
5-noid with cyclic symmetry.
8-noid with dihedral symmetry.
4-noid with tetrahedral symmetry.
6-noid with octahedral symmetry.
8-noid with octahedral symmetry.
12-noid with icosahedral symmetry.
20-noid with icosahedral symmetry.

References

  1. N. Schmitt, M. Kilian, S.-P. Kobayashi and W. Rossman, Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms, J. Lond. Math. Soc. (2) 75 (2007), no. 3, 563–581.
  2. N. Schmitt, Constant mean curvature n-noids with platonic symmetries, arxiv:math/0702469, 2007.