The western honey bee (Apis mellifera) is a domesticated pollinator famous for living in highly social colonies. In the spring, thousands of worker bees and a queen fly from their hive in search of a new home. They self-assemble into a swarm that hangs from a tree branch for several days. We reconstruct the non-isotropic arrangement of worker bees inside swarms made up of 3000 - 8000 bees using x-ray computed tomography. Some bees are stationary and hang from the attachment board or link their bodies into hanging chains to support the swarm structure. The remaining bees use the chains as pathways to walk around the swarm, potentially to feed the queen or communicate with one another. The top layers of bees bear more weight per bee than the remainder of the swarm, suggesting that bees are optimizing for additional factors besides weight distribution. Despite not having a clear leader, honey bees are able to organize into a swarm that protects the queen and remains stable until scout bees locate a new hive.