In the Floating Silicon Method (FSM), a single-crystal Si ribbon is grown while floating on the surface of a Si melt. In this paper, we describe the phenomenology of FSM, including the observation of approximately regularly spaced "facet lines" on the ribbon surface whose orientation aligns with (111) crystal planes. Sb demarcation experiments sectioned through the thickness of the ribbon reveal that the solid/melt interface consists of dual (111) planes and that the leading edge facet growth is saccadic in nature, rather than steady-state. To explain this behavior, we propose a heuristic solidification limit cycle theory, using a continuum level of description with anisotropic kinetics as developed by others, and generalizing the interface kinetics to include a roughening transition as well as a re-faceting mechanism that involves curvature and the Gibbs Thomson effect. (C) 2016 Elsevier B.V. All rights reserved.