4 papers
Sparse groups need not be semisparse
Isabel Hubard, Micael Toledo
In 1999 Michael Hartley showed that any abstract polytope can be constructed as a double coset poset, by means of a C-group $\C$ and a subgroup $N \leq \C$. Subgroups $N \leq \C$ t…
Colorful Associahedra and Cyclohedra
Gabriela Araujo-Pardo, Isabel Hubard, Deborah Oliveros +1
Every n-edge colored n-regular graph G naturally gives rise to a simple abstract n-polytope, the colorful polytope of G, whose 1-skeleton is isomorphic to G. The paper describes co…
Symmetric Graphicahedra
Maria Del Rio-Francos, Isabel Hubard, Deborah Oliveros +1
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 gra…
Colorful Polytopes and Graphs
Gabriela Araujo-Pardo, Isabel Hubard, Deborah Oliveros +1
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 abstra…