Hierarchical relations are prevalent and indispensable for organizing human\nknowledge captured by a knowledge graph (KG). The key property of hierarchical\nrelations is that they induce a partial ordering over the entities, which needs\nto be modeled in order to allow for hierarchical reasoning. However, current KG\nembeddings can model only a single global hierarchy (single global partial\nordering) and fail to model multiple heterogeneous hierarchies that exist in a\nsingle KG. Here we present ConE (Cone Embedding), a KG embedding model that is\nable to simultaneously model multiple hierarchical as well as non-hierarchical\nrelations in a knowledge graph. ConE embeds entities into hyperbolic cones and\nmodels relations as transformations between the cones. In particular, ConE uses\ncone containment constraints in different subspaces of the hyperbolic embedding\nspace to capture multiple heterogeneous hierarchies. Experiments on standard\nknowledge graph benchmarks show that ConE obtains state-of-the-art performance\non hierarchical reasoning tasks as well as knowledge graph completion task on\nhierarchical graphs. In particular, our approach yields new state-of-the-art\nHits@1 of 45.3% on WN18RR and 16.1% on DDB14 (0.231 MRR). As for hierarchical\nreasoning task, our approach outperforms previous best results by an average of\n20% across the three datasets.\n