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This is an investigation of the role of shuffling and concatenating in thetheory of graph drawing. A simple syntactic description of these and relatedoperations is proved complete in the context of finite partial orders, asgeneral as possible. An explanation based on that is given for a previouslyinvestigated collapse of the permutohedron into the associahedron, and forcollapses into other less familiar polyhedra, including the cyclohedron. Suchpolyhedra have been considered recently in connection with the notion oftubing, which is closely related to tree-like finite partial orders definedsimply and investigated here in detail. Like the associahedron, some of theseother polyhedra are involved in categorial coherence questions, which will betreated in a sequel to this paper. (Printed versions of our papers havesometimes been spoiled by referees and editorial assistants, and the versionsposted here in the arXiv are always to be preferred. However, due to theirresponsible refereeing and the massive and misguided editorial assistancecommissioned by Cambridge University Press, the text of the present paperprinted in the journal "Mathematical Structures in Computer Science", whereeven the title has been changed without our consent, is such that we can bearresponsibility only for the text posted here in the arXiv.)

Shuffles and Concatenations in Constructing of Graphs