Trinoids with Constant Mean Curvature
Trinoids with constant mean curvature are a family of surfaces that depend on the parameters , related to the monodromy group. When , the trinoid is symmetric . The trinoid is embedded when and the parameter is related to the embeddedness. The equations are derived from Bryant holomorphic representation (analogous to the Weierstrass representation of minimal surfaces), in terms of gamma and hypergeometric functions.
To be closed, the trinoids must simultaneously satisfy the following conditions:
 A. I. Bobenko, T. V. Pavlyukevich, and B. A. Springborn, "Hyperbolic Constant Mean Curvature One Surfaces: Spinor Representation and Trinoids in Hypergeometric Functions." lanl.arxiv.org/abs/math/0206021v2.