2012/10/07 by Anthony M. Cutler, Cutler, Anthony M., Egon Schulte +3
Mathematics · #51M20 #52B15 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #math.CO #math.MG #msc:51M20 #msc:52B15
paper · pdf · doi:10.48550/arxiv.1210.2064
8 pages; Contributions to Algebra and Geometry (to appear)
arxiv created 2012/10/07 · arxiv updated 2012/10/09
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.