On octahedral fulleroids

On octahedral fulleroids

The discovery of the fullerene has raised an interest in the study of other candidates for modeling of carbon molecules. Motivated by works of P. Fowler, Delgado Friedrichs and Deza, Oh(a, b)-fulleroids were defined as cubic convex polyhedra having only a-gonal and bgonal faces and the symmetry group isomorphic with the full symmetry group of regular octahedron. In this paper we give sufficient...

Fantasmagoric Fulleroids Revisited

New strange fulleroids are built up by using the three classical composite map operations: tripling (leapfrog Le), quadrupling (chamfering Q) and septupling (capra Ca) on the starting structure dodecahedron. These transforms belong to the icosahedral symmetry group and show interesting mathematical and (possible) physico-chemical properties. Topological symmetry data of the presented cages are ...

More icosahedral fulleroids

Octahedral and Dodecahedral Monopoles

It is shown that there exists a charge five monopole with octahedral symmetry and a charge seven monopole with icosahedral symmetry. A numerical implementation of the ADHMN construction is used to calculate the energy density of these monopoles and surfaces of constant energy density are displayed. The charge five and charge seven monopoles look like an octahedron and a dodecahedron respectivel...

Small Octahedral Systems

We consider set systems that satisfy a certain octahedral parity property. Such systems arise when studying the colourful simplices formed by configurations of points of in R; configurations of low colourful simplicial depth correspond to systems with small cardinality. This construction can be used to find lower bounds computationally for the minimum colourful simplicial depth of a configurati...