Icosahedral Skeletal Polyhedra Realizing Petrie Relatives of Gordan's   Regular Map
  Every regular map on a closed surface gives rise to generally six regular maps, its "Petrie relatives", that are obtained through iteration of the duality and Petrie operations (taking duals and Petrie-duals). It is shown that the skeletal polyhedra in Euclidean 3-space which realize a Petrie relative of the classical Gordan regular map and have full icosahedral symmetry, comprise precisely four infinite families of polyhedra, as well as four individual polyhedra. 
Anthony M. Cutler, Egon Schulte and Jorg M. Wills
math.CO math.MG