The faceting of monocrystals of the lyotropic cubic liquid crystals in equi
librium with a humid atmosphere is observed. Experiments reveal the presenc
e of more than 60 different types of facets on the surface of a spherical c
rystal of radius R = I mm. The devil's staircase type of faceting has been
predicted theoretically when the interaction between steps on the crystal s
urface is repulsive.