  A quantum superintegrable model with reflections on the 2-sphere is
introduced. Its two algebraically independent constants of motion generate a
central extension of the Bannai--Ito algebra. The Schrodinger equation
separates in spherical coordinates and its exact solutions are presented. It is
further observed that the Hamiltonian of the system arises in the addition of
three representations of the sl_{-1}(2) algebra (the dynamical algebra of the
one-dimensional parabosonic oscillator). The contraction from the two-sphere to
the Euclidean plane yields the Dunkl oscillator in two dimensions and its
Schwinger-Dunkl symmetry algebra sd(2).
