In this letter, we introduce a new soft biomimetic optical tactile sensor based on mimicking the interlocking structure of the epidermal-dermal boundary: the BioTacTip. The primary sensing unit comprises a sharp white tip surrounded by four black cover tips that when subjected to an external force emphasizes the applied direction and contact location, for high-resolution imaging by an internal camera. The sensor design means that we can utilize the tactile images directly as the model input (not requiring marker detection) for computationally efficient reconstruction of 3D external forces, contact geometry, localization and depth, by utilizing an analytic tactile model based on dynamic friction and internal pressure. Indentation and press-and-shear tests confirmed this mechanism, with sub-mm localization and indentation errors, and normal and shear force time series that match measured quantities. The sensor design opens up a new way to instantiate biomimicry in optical tactile sensors that utilizes mechanical processing in the skin.