Dr. Thomas P. Connelly

Invariant Projections on Cycle Spaces of Polyhedral Graphs: An Orbit-Count Formula and a Characterisation of the Regular Solids

Abstract Let Γ be the skeleton of a convex polyhedron, with cycle space H₁(Γ) and cut space K(Γ), and set c(Γ) = dim Hom_{Aut(Γ)}(H₁(Γ), K(Γ)). By a theorem of Dilworth, Kutzarova and Ostrovskii, c(Γ) = 0 is equivalent to uniqueness of the invariant projection of the signed edge...

Invariant Projections on Cycle Spaces of Polyhedral Graphs: An Orbit-Count Formula and a Characterisation of the Regular Solids

Abstract Let Γ be the skeleton of a convex polyhedron, with cycle space H₁(Γ) and cut space K(Γ), and set c(Γ) = dim Hom_{Aut(Γ)}(H₁(Γ), K(Γ)). By a theorem of Dilworth, Kutzarova and Ostrovskii, c(Γ) = 0 is equivalent to uniqueness of the invariant projection of the signed edge...