Geodesic
Symmetric graphicahedra
Ars mathematica contemporanea, Volume 5 (2012) no. 2, pp. 383-405

See the original article notice from the Ars Mathematica Contemporanea website source

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 Ãq − 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.
DOI: 10.26493/1855-3974.203.7ba
Keywords: Edge colouring, polytopes, Cayley graps 
María Del Río Francos; Isabel Hubard; Deborah Oliveros; Egon Schulte. Symmetric graphicahedra. Ars mathematica contemporanea, Volume 5 (2012) no. 2, pp. 383-405. doi: 10.26493/1855-3974.203.7ba
@article{10_26493_1855_3974_203_7ba,
     author = {Mar{\'\i}a Del R{\'\i}o Francos and Isabel Hubard and Deborah Oliveros and Egon Schulte},
     title = {
		{Symmetric} graphicahedra
	},
     journal = {Ars mathematica contemporanea},
     pages = {383--405},
     year = {2012},
     volume = {5},
     number = {2},
     doi = {10.26493/1855-3974.203.7ba},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.203.7ba/}
}
TY  - JOUR
AU  - María Del Río Francos
AU  - Isabel Hubard
AU  - Deborah Oliveros
AU  - Egon Schulte
TI  - Symmetric graphicahedra
	
JO  - Ars mathematica contemporanea
PY  - 2012
SP  - 383
EP  - 405
VL  - 5
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.203.7ba/
DO  - 10.26493/1855-3974.203.7ba
LA  - en
ID  - 10_26493_1855_3974_203_7ba
ER  - 
%0 Journal Article
%A María Del Río Francos
%A Isabel Hubard
%A Deborah Oliveros
%A Egon Schulte
%T Symmetric graphicahedra
	
%J Ars mathematica contemporanea
%D 2012
%P 383-405
%V 5
%N 2
%U http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.203.7ba/
%R 10.26493/1855-3974.203.7ba
%G en
%F 10_26493_1855_3974_203_7ba

Cited by Sources: