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  • Symmetric graphicahedra
    Río Francos, María del ...
    Given a connected graph ▫$G$▫ with ▫$p$▫ vertices and ▫$q$▫ edges, the ▫$G$▫-graphicahedron is a vertex-transitive simple abstract polytope of rank ▫$q$▫ whose edge-graph is isomorphic to a Cayley ... graph of the symmetric group ▫$S_p$▫ associated with ▫$G$▫. The paper explores combinatorial symmetry properties of ▫$G$▫-graphicahedra, focussing in particular on transitivity properties of their automorphism groups. We present a detailed analysis of the graphicahedra for the ▫$q$▫-star graphs ▫$K_1{,q}$▫ and the ▫$q$▫-cycles ▫$C_q$▫. The ▫$C_q$▫-graphicahedron is intimately related to the geometry of the infinite Euclidean Coxeter group ▫$\tilde{A}_{q - 1}$▫ and can be viewed as an edge-transitive tessellation of the ▫$(q - 1)$▫-torus by ▫$(q - 1)$▫-dimensional permutahedra, obtained as a quotient, modulo the root lattice ▫$A_{q - 1}$▫, of the Voronoi tiling for the dual root lattice ▫$A_{q - 1}^\ast$▫ in Euclidean ▫$(q- 1)$▫-space.
    Vir: Ars mathematica contemporanea : SIGMAP 2010 (Vol. 5, no. 2, 2012, str. 383-405)
    Vrsta gradiva - prispevek na konferenci
    Leto - 2012
    Jezik - angleški
    COBISS.SI-ID - 16439385

    Povezava(-e):

    http://amc.imfm.si/index.php/amc/article/view/203/199

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