symbol

The basic structures have a three-letter code e.g. srs for the SrSi2 net and dia for the diamond net.

Some derived structures are designated thus (see below for definitions)

-a augmented net

-b binary net

-c catenated pair

-d dual

-e edge net

-f, -g etc. decorated nets

-x extended coordination

-z alternative configuration

augmented net is one in which the vertices of the original net are replaced by a polygon or polyhedron corresponding to the original coordination figure. The net (cab) named for CaB6 is the augmented primitive cubic (pcu) net and can also be found using the symbol pcu-a.

binary net is one derived from a uninodal net with even rings by alternating vertices AB such that A is bonded only to B and vice versa. The sphalerite structure of ZnS is the binary version of diamond (dia-b).

catenated net refers to a pair of self-dual nets (such as diamond) intergrown. Notice that the symmetry of the pair is different from that of just one.

dual net is the net of the tiling dual the natural tiling of the first net. This is the same net in the case of self-dual nets. E.g. dia-d = dia.

edge net (also expanded net) is obtained from the original net by placing vertices in the middle of the edges, discarding the original vertices and edges, and joining the new vertices to enclose the coordination figure of the original vertices.

decorated nets are obtained by replacing the vertices of the original net by groups of vertices. Augmented nets are special cases of decorated nets. (To see examples enter bcu.)

extended coordination Occasionally one want to consider other than nearest neighbors in the coordination shell. An example is provided by the body-centered cubic lattice. Each vertex has eight first neighbors and 6 second neighbors. The structure bcu is eight-coordinated and is the dual of nbo. bcu-x is 14-coordinated and is the dual of sod. [bcu-x is the structure corresponding to a vertex- and tile-transitive tiling of space by tetrahedra.

alternative configuration Sometimes an configuration other than the maximum volume is of interest. See for example the configuration (ths-z) of the 3-coordinated ths net with the three edges meeting at a vertex forming a T shape.

References: Delgado-Friedrichs, O.; O'Keeffe, M.; Yaghi, O. M. Acta Crystallogr. A 2003, 59, 22-27 and 515-525.