  We present the results of an investigation into the representations of
Archimedean polyhedra (those polyhedra containing only one type of vertex
figure) as quotients of regular abstract polytopes. Two methods of generating
these presentations are discussed, one of which may be applied in a general
setting, and another which makes use of a regular polytope with the same
automorphism group as the desired quotient. Representations of the 14 sporadic
Archimedean polyhedra (including the pseudorhombicuboctahedron) as quotients of
regular abstract polyhedra are obtained, and summarised in a table. The
information is used to characterise which of these polyhedra have acoptic
Petrie schemes (that is, have well-defined Petrie duals).
