Coordination polygons

At the vertices of a coordination polyhedron of a given atom (in addition to atoms of different elements) there can also be atoms of the same kind. A considerable variety of coordination polyhedra exists. In some cases, plane coordination polygons have to be considered. The number of vertices may vary from 3 to 24. Generally, the structure consists of atoms with different coordination numbers according to Kripyakevich, structures are most conveniently classified according to the type of coordination polyhedron of the atoms with the lowest coordination number. 

Swiegers, G. F. and Malefetse, T. J., Classification of coordination polygons and polyhedra according to their mode of self-assembly , Chem. Eur. J. 2001, 7, 3637-3643. 

The site symmetry term indicates the idealized geometry of the central atom and is a letter code derived from the geometric terms used to describe the coordination polygon. The coordination number is given to define further the site symmetry... 

Swiegers, G.F. Malafetse. T.J. Classification of coordination polygons and polyhedra according to their mode of self-assembly. Chem. Eur. J. 2001, 7. 3637-3643. Swiegers, G.F. Malefetse. T.J. Classification of coordination polygons and polyhedra according to their mode of self-assembly. 2. Review of the literature. Coord. Chem. Rev. 2002. 225, 91-121. 

Stmctural design principles for self-assembled coordination polygons and polyhedra 13CC1354. 

Another series of compounds which fully satisfy this rule are the minerals of silicates type for which, the tetrahedra, as coordinated polygons for cations of silicon tend to couple in a minimal way, according to the Rules 3 and 4, see for example the series of Table 4.13. 

Coordination as the motif in the rational design of supramolecular metallacyclic polygons and polyhedra 97ACR502. 

The grid in view is supposed to be connected, it being understood that any two inner nodes can be joined by a polygonal line, the parts of which are parallel to the coordinate axes and vertices coincide with inner nodes of the grid. Then at least one of the four nodes a = 1,2, of... 

The difference between V- and D-tessilations is as follows each of V-polyhedra includes one network point (or particle) and a void that is closer to this point than to others, each of D-polyhedra includes one cavity and parts of the particles that are the closest to the center of the cavity and all windows that are on the borders with other neighboring cavities. It is convenient to term the latter as PBU/C, where C means cavity. The local coordination number of cavities Zc is equal to the number of the faces of PBU/C (D-polyhedra or D-polygons), and their local porosity e (or eA in 2D space) is equal to the unoccupied volume. Typical D-polyhedra are shown in Figure 9.30 and Figure 9.31. 

WoWj/2 the body-centred cubic structure of W (1 atom in 0, 0, 0 and 1 atom in A, A, /) corresponds to a sequence of type 1 and type 4 square nets at the heights 0 and A, respectively. Note, however, that for a fall description of the structure, either in the hexagonal or the tetragonal case, the inter-layer distance must be taken into account not only in terms of the fractional coordinates (that is, the c/a axial ratio must be considered). For more complex polygonal nets, their symbolic representation and use in the description, for instance, of the Frank-Kasper phases, see Frank and Kasper (1958) and Pearson (1972). 

As stated, the Platonic solids constitute a family of five convex uniform polyhedra made up of the same regular polygons and possess either 32, 432, or 532 symmetry. As a result, the three coordinate directions within each solid are equivalent, which makes these polyhedra models for spheroid design. 

Protein PDB code Site Coordinating peptide No. of coordinating ligands No. of coordinating waters No. of bidentate ligands Root mean square deviation of ligands from ideal polygon" (A) j Ca2 + (M)" Reference for affinity data... 

Stang, P.J. and Olenyuk, B. (1997) Self-assembly, symmetry, and molecular architecture Coordination as the motif in the rational design of supramolecular metallacyclic polygons and polyhedra. Acc. Chem. Res.. 30 (12), 502-518. 

Coordination polyhedron. It is standard practice to think of the lignnd atoms that are directly attached to the central atom as defining, i coordination polyhedron (or polygon) about the central atom. Thus Co(NH,)h]J+ is an octahedral ion and [PtCIJ2- is a square planar ion. In this way the coordination number may equal the number of vertices in (he coordination polyhedron. Exceptions are common among orgunonietnlhtf compounds. 

Different geometrical arrangements of the atoms attached to the central atom are possible for all coordination numbers greater than one. The coordination polyhedron (or polygon in planar molecules) may be denoted in the name by an affix called the polyhedral symbol. This descriptor clearly distinguishes isomers differing in the geometries of their coordination polyhedra. 

Fig. 2.1. A random walk chain of 50 monomers of fixed length (thin polygon), leaking the position of every fifth monomer as segment coordinates, we find our model chain (fal polygon), which is approximated by a Gaussian coil...

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