The honeybee dance "language" is one of the most popular examples of information transfer in the animal world. Today, more than 60 years after its discovery it still remains unknown how follower bees decode the information contained in the dance. In order to build a robotic honeybee that allows a deeper investigation of the communication process we have recorded hundreds of videos of waggle dances. In this paper we analyze the statistics of visually captured high-precision dance trajectories of European honeybees (Apis mellifera carnica). The trajectories were produced using a novel automatic tracking system and represent the most detailed honeybee dance motion information available. Although honeybee dances seem very variable, some properties turned out to be invariant. We use these properties as a minimal set of parameters that enables us to model the honeybee dance motion. We provide a detailed statistical description of various dance properties that have not been characterized before and discuss the role of particular dance components in the commmunication process.