keywords

 

keywords

chiral

This selects all structures from chiral space groups (those with only proper operations, viz. rotation, screw or translation).

chathrate

This term is used to refer to 4-coordinated nets based on simple tilings by polyhedra with faces with up to 6 sides. mtn and mep are the nets of types I and II clathrate hydrates.

good

"good" structures have all shortest distances corresponding to equal lengths and the next shortest distance > 1.4 times as large, and/or have the order of the point symmetry at the vertices > 7.

heterocoord

This refers to mixed coordination (e.g. 4- and 8- coordinated). for 3,4-, 3,6- and 4,6-coordinated use the keywords "heterocoord 34", "heterocoord 36" and "heterocoord 46".

infinite polyhedron

An infinite polyhedron is a tiling of a 3-periodic surface. See O'Keeffe, M.; Hyde, B. G. Crystal Structures I: Patterns and Symmetry. Washington. Mineral. Soc. Am. (1996). We have not systematically searched for these.

interpenetrating net

These are structure with two, or more, interpenetrating nets of the same kind. Note that the symmetry is generally different from that of a single net. These all have symbols ending in -c or –cn. The means there are n (>2) interpenetrating nets.

isohedral tiling

These are structures for which the normal tiling consists of one kind of tile with all tiles related by a symmetry operation (tile transitive).

polar

This selects nets with polar symmetry (i.e. those of classes 1, 2, m, 3, 3m, 4, 4m, 6, 6m).

regular net

There are 5 regular nets in which the vertices have a regular polygon or polyhedron as vertex figure. For their natural tilings the transitivity is 1111. Delgado-Friedrichs, O. F.; O'Keeffe, M.; Yaghi, O. M. Acta Crystallogr. 2003, A59, 22-27. [transitivity pqrs means p kinds of vertex, q kinds of edge, r kinds of tile face, s kinds of tile]

rod net

In rod nets vertices lie on straight, non-intersecting lines.

self dual net

A self-dual net is a net that has a tin that tiling is self-dual. In some cases the self-dual tiling is not the natural one and is given in parentheses in "tiling".

semiregular net

Semiregular nets have one kind of vertex and one kind of edge (vertex and edge transitive, or transitivity 11rs) Delgado-Friedrichs, O. F.; O'Keeffe, M.; Yaghi, O. M. Acta Crystallogr. 2003, A59, 515-525.

simple tiling

In a simple tiling 2 tiles meet at a face, 3 at an edge and 4 at a vertex. the tiles are simple polyhedra (1 faces meet at each edge and 3 at each vertex). There are nine vertex-transitive simple tilings [choose keyword "simple tiling" and nets with one kind of vertex]. Their duals are the nine ways of tiling space with congruent polyhedra. See Delgado-Friedrichs, O.; Huson, D. H. Discr. Comp. Geom. 1999, 21, 299-315. Delgado-Friedrichs, O.; O'Keeffe, M. Acta Cryst. 2005, A61, 358-362.

uniform net

In a uniform net the shortest rings contained in each angle are the same size. See especially A. F. Wells, Three dimensional nets and polyhedra. Wiley, New York 1977.

uniform tiling

In a uniform tiling, all the vertices are the same (uninodal or vertex transitive) and the tiles are all uniform polyhedra (vertex transitive with regular polygonal faces). Grünbaum, B. Geombinatorics 1994, 4, 49-56. Deza, M.; Shtogrin, M. Eur. J. Combinatorics 2000, 21, 807-814.

The correspondence with Grünbaum's numbers are: 1: fcu  2: hcp  3: tcd  4: tca  5: flu-e  6:  crs  7: reo  8: cab  9: reo-e  10: ubt  11: hex  12: tsi  13:  svk  14: sve  15: svh  16: tfs  17: svj  18: kag  19: ttw  20: pcu-i  21: hal  22: pcu  23: fst  24: fee  25: lta  26: hex  27: rho  28: sod

zeolite net

These nets appear in the Atlas of Zeolite Structure Types http://www.iza-structure.org/databases/. Note that we always use a maximum symmetry configuration. Generally we only include zeolite nets with one or two kinds of vertex.