This is an investigation of the role of shuffling and concatenating in the
theory of graph drawing. A simple syntactic description of these and related
operations is proved complete in the context of finite partial orders, as
general as possible. An explanation based on that is given for a previously
investigated collapse of the permutohedron into the associahedron, and for
collapses into other less familiar polyhedra, including the cyclohedron. Such
polyhedra have been considered recently in connection with the notion of
tubing, which is closely related to tree-like finite partial orders defined
simply and investigated here in detail. Like the associahedron, some of these
other polyhedra are involved in categorial coherence questions, which will be
treated in a sequel to this paper.