  A special case of the Gaudin model related to the superalgebra $osp(1,2)$ is
investigated. An exact solution for the model in the spin-1/2 representation is
presented. A complete set of commuting observables is diagonalized and the
corresponding eigenvectors and eigenvalues are explicitly calculated. The
approach used in this paper is based on the co-algebra symmetry of the model,
already known from the spin-1/2 Calogero-Gaudin system.
