naa a22 4500 510736939 CHVBK 20180411083013.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s13366-012-0124-4 doi (NATIONALLICENCE)springer-10.1007/s13366-012-0124-4 Icosahedral skeletal polyhedra realizing Petrie relatives of Gordan's regular map [Elektronische Daten] [Anthony Cutler, Egon Schulte, Jörg Wills] 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. The Managing Editors, 2012 Regular polyhedra nationallicence Geometric graphs nationallicence Regular maps on surfaces nationallicence Gordan's map nationallicence Abstract polytopes nationallicence Cutler Anthony Boston, MA, USA aut Schulte Egon Northeastern University, 02115, Boston, MA, USA aut Wills Jörg University of Siegen, 57068, Siegen, Germany aut Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer Berlin Heidelberg 54/2(2013-10-01), 651-657 0138-4821 54:2<651 2013 54 13366 https://doi.org/10.1007/s13366-012-0124-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13366-012-0124-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cutler Anthony Boston, MA, USA aut NATIONALLICENCE 700 1- Schulte Egon Northeastern University, 02115, Boston, MA, USA aut NATIONALLICENCE 700 1- Wills Jörg University of Siegen, 57068, Siegen, Germany aut NATIONALLICENCE 773 0- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer Berlin Heidelberg 54/2(2013-10-01), 651-657 0138-4821 54:2<651 2013 54 13366 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer