The problem of finding good mappings is central to designing and executing applications efficiently in embedded systems. In heterogeneous multicores, which are ubiquitous today, this problem yields an intractably large design space of possible mappings. Most methods explore this space using heuristics, many of which implicitly use geometric notions in mappings. In this paper we explore the geometry of the mapping problem explicitly, for finding embeddings of the mapping space that capture its structure. This allows us to formulate new mapping strategies by leveraging the geometry of the mapping space, as well as improving existing heuristics that do so implicitly. We evaluate our approach on a novel mapping heuristic based on gradient descent, as well as multiple existing meta-heuristics. For complex architectures, our methods improved the results of established exploration meta-heuristics by about an order of magnitude in average.