Topological density of nets: a direct calculation.
The topological density of a three-dimensional net is currently available after determining its entire coordination sequence. This paper shows that its value can be obtained directly from the set of cycles of the quotient graph of the net. A geometrical tool, the cycles figure of the net has been developed for this purpose. Its construction as a convex polyhedron with triangular faces is described as well as its use for topological density calculations. An exact expression is derived for three-dimensional nets and extended to arbitrary n-dimensional nets. Additionally, this paper describes applications to three-dimensional lattices and nets, n-dimensional diamonds and lonsdaleites.
Eon
Jean Guillaume
JG
Instituto de Química, Universidade Federal do Rio de Janeiro, A-631 Cidade Universitária, Ilha do Fundão, Rio de Janeiro, 21945-970 Brazil. jgeon@iq.ufrj.br