In this letter, we explore the potential energy surface (PES) of the 3×3 C-face of SiC by means of density functional theory. Following an extensive and intuitive exploration, we propose a model for this surface reconstruction based on an all-silicon over-layer forming an ordered honeycomb-kagome network. This model is compared to the available experimental Scanning Tunneling Microscope (STM) topographies and conductance maps. Our STM simulations reproduce the three main characteristics observed in the measurements, revealing the underlying complex and hybrid passivation scheme. Indeed, below the ordered over-layer, the competition between two incompatible properties of silicon induces a strong disorder in the charge transfer between unpassivated dangling bonds of different chemistry. This effect, in conjunction with the glassy-like character of the PES, explain why it took decades to explain this structure.