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 3 He crystals at the temperature of 0.55 mK by using a unique lowtemperature Fabry-Pé rot 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 3 He 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.T he crystals that we find in nature have usually a polyhedral shape. Their surface is covered with smooth faces or facets that correspond to high-symmetry crystallographic orientations (see Fig. 1). These facets have developed on the crystal surfaces during growth when the crystals were formed. It must be pointed out that it is difficult to study the growth dynamics as well as the equilibrium shape of ordinary crystals. The difficulties are caused by big differences in entropy and density between the solid and the adjacent melt or vapor phases and finite thermal conductivities of these bulk phases. As a result, the relaxation processes are highly dissipative and the corresponding time scales extremely long. The equilibrium shapes have therefore been obtained with microscopic metallic crystals which after annealing of several days have showed facets surrounded by rough (rounded) areas on their surface (1).It was predicted by Landau in the middle of the last century that, in the limit of low temperatures, any ideal crystal should be completely faceted, with an infinite number of facets on its surface (2). This is the so-called ''devil's staircase '' phenomenon (3, 4). The most complicated crystals, however, have shown at most six types of facets. Only very recently Pieranski and his coworkers (5) were able to grow lyotropic monocrystals that revealed more than 60 types of facets on their surface, confirming experimentally the devil's staircase phenomenon. They interpreted their results as the coincidence of a quite large surface tension and interplanar distance with an exceptionally low elastic modulus. But with liquid lyotropic crystals, faceting can be studied in a very limited temperature range and it is hard to measure their equilibrium shape.The experimental situation is more promising in helium crystals, which exist at low temperatures and high pressures. The dynamics of helium crystals, which are surrounded by a superfluid with high thermal conductivity, can be extremely fast. For instance, 4 He crystals...