Hyperbolic constant mean curvature one surfaces: Spinor representation   and trinoids in hypergeometric functions
  We present a global representation for surfaces in 3-dimensional hyperbolic space with constant mean curvature 1 (CMC-1 surfaces) in terms of holomorphic spinors. This is a modification of Bryant's representation.   It is used to derive explicit formulas in hypergeometric functions for CMC-1 surfaces of genus 0 with three regular ends which are asymptotic to catenoid cousins (CMC-1 trinoids). 
Alexander I. Bobenko, Tatyana V. Pavlyukevich, Boris A. Springborn