  The orientals or oriented simplexes are a family of strict omega-categories
constructed by Ross Street. We show that the category of orientals is
isomorphic to a subcategory of the category of chain complexes. This leads to a
very simple combinatorial description of the morphisms between orientals. We
also show that the category of orientals is the closure of the category of
simplexes under certain filler operations which represent complicial
operations.
