naa a22 4500 510782841 CHVBK 20180411083253.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s11856-012-0136-7 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0136-7 Colorful polytopes and graphs [Elektronische Daten] [Gabriela Araujo-Pardo, Isabel Hubard, Deborah Oliveros, Egon Schulte] The paper investigates connections between abstract polytopes and properly edge colored graphs. Given any finite n-edge-colored n-regular graph G, we associate to G a simple abstract polytope P G of rank n, the colorful polytope of G, with 1-skeleton isomorphic to G. We investigate the interplay between the geometric, combinatorial, or algebraic properties of the polytope P G and the combinatorial or algebraic structure of the underlying graph G, focussing in particular on aspects of symmetry. Several such families of colorful polytopes are studied including examples derived from a Cayley graph, in particular the graphicahedra, as well as the flagadjacency polytopes and related monodromy polytopes associated with a given abstract polytope. The duals of certain families of colorful polytopes have been important in the topological study of colored triangulations and crystallization of manifolds. Hebrew University Magnes Press, 2013 Araujo-Pardo Gabriela Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Cientifica, Circuito Exterior, Ciudad Universitaria, Coyoacán, 04510, México, D. F., México aut Hubard Isabel Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Cientifica, Circuito Exterior, Ciudad Universitaria, Coyoacán, 04510, México, D. F., México aut Oliveros Deborah Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Cientifica, Circuito Exterior, Ciudad Universitaria, Coyoacán, 04510, México, D. F., México aut Schulte Egon Department of Mathematics, Northeastern University, 02115, Boston, MA, USA aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 647-675 0021-2172 195:2<647 2013 195 11856 https://doi.org/10.1007/s11856-012-0136-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0136-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Araujo-Pardo Gabriela Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Cientifica, Circuito Exterior, Ciudad Universitaria, Coyoacán, 04510, México, D. F., México aut NATIONALLICENCE 700 1- Hubard Isabel Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Cientifica, Circuito Exterior, Ciudad Universitaria, Coyoacán, 04510, México, D. F., México aut NATIONALLICENCE 700 1- Oliveros Deborah Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Cientifica, Circuito Exterior, Ciudad Universitaria, Coyoacán, 04510, México, D. F., México aut NATIONALLICENCE 700 1- Schulte Egon Department of Mathematics, Northeastern University, 02115, Boston, MA, USA aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 647-675 0021-2172 195:2<647 2013 195 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer