  We investigate the ground-state phases of a mixture of spin-1 and spin-2
Bose-Einstein condensates at zero magnetic field. In addition to the intra-spin
interactions, two spin-dependent interaction coefficients are introduced to
describe the inter-spin interaction. We systematically explore the wide
parameter space, and obtain phase diagrams containing a rich variety of phases.
For example, there exists a phase in which the spin-1 and spin-2 vectors are
tilted relative to each other breaking the axial symmetry.
