It has been predicted by Landau that, ideally at low temperatures, crystals should show many different types of facets, i.e., flat smooth faces on their surface, but this so-called "devil's staircase" phenomenon has been difficult to observe experimentally. In this paper we describe our recent experiments, in which altogether 11 different types of facets have been identified on growing He-3 crystals at the temperature of 0.55 mK by using a unique low-temperature Fabry-Perot interferometer. Previously only 3 types of facets had been seen in this system. We have also measured the growth velocities of different facets, and our interpretation of the obtained results yields the conclusion that He-3 has much stronger coupling of the liquid-solid interface to the crystal lattice than has been expected. After an introduction we present a short theoretical background about the equilibrium crystal shape and the roughening transitions, which is followed by the description of our experimental results and discussion.