2012/06/23 by Maria Del Rio-Francos, Maria Del Río-Francos, Del Rio-Francos, Maria +7
Biochemistry, Genetics and Molecular Biology · Mathematics · #51M20 #52B15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Metric Geometry (math.MG) #Ocular Disorders and Treatments #math.CO #math.MG #msc:51M20 #msc:52B15
paper · pdf · doi:10.48550/arxiv.1206.5420
Ars Mathematica Contemporanea (to appear, 29 pages)
arxiv created 2012/06/23 · openalex publication_date 2012/06/23 · arxiv updated 2012/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Sp 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 K1,q and the q-cycles Cq. The Cq-graphicahedron is intimately related to the geometry of the infinite Euclidean Coxeter group Aq-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 Aq-1, of the Voronoi tiling for the dual root lattice Aq-1^* in Euclidean (q-1)-space.