CHEMISTRY: Networked Polyhedra

Polyhedra in (inorganic) chemistry.

A systematic description of polyhedra with varying degrees of regularity is illustrated with examples of chemical structures, mostly from different fields of Inorganic Chemistry. Also the geometrical relationships between different polyhedra are highlighted and their application to the analysis of complex structures is discussed.

Reticular chemistry of metal-organic polyhedra.

Metal-organic polyhedra (MOPs), are discrete metal-organic molecular assemblies. They are useful as host molecules that can provide tailorable internal volume in terms of metrics, functionality, and active metal sites. As a result, these materials are potentially useful for a variety of applications, such as highly selective guest inclusion and gas storage, and as nanoscale reaction vessels. Th...

polyhedra ∗

Graphs of polyhedra; polyhedra as graphs

Relations between graph theory and polyhedra are presented in two contexts. In the first, the symbiotic dependence between 3-connected planar graphs and convex polyhedra is described in detail. In the second, a theory of nonconvex polyhedra is based on a graph-theoretic foundation. This approach eliminates the vagueness and inconsistency that pervade much of the literature dealing with polyhedr...

Cubic Polyhedra

A cubic polyhedron is a polyhedral surface whose edges are exactly all the edges of the cubic lattice. Every such polyhedron is a discrete minimal surface, and it appears many (but not all) of them can be relaxed to smooth minimal surfaces (under an appropriate smoothing flow, keeping their symmetries). Here we give a complete classification of the cubic polyhedra. Among these are five new infi...