By P. G. Ciarlet, Jacques Louis Lions, Philippe G. Ciarlet
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In turn, the lvt topology describes a partial ring net for the gis atomic net, and so on. 3 Role of Geometrical and Coordination Parameters The criteria of high symmetry are not sufﬁcient to explain an important role of some ‘‘default’’ nets. For example, the net sra has rather low symmetry (Imma), not minimal transitivity (33), does not belong to the special classes mentioned above, and its nodes are not allocated in the most symmetrical positions in the space group (8i with site symmetry m). However, sra occupies the second place after dia in the list of the most frequent MOF topologies with tetrahedral units , while two nets following after it – sod (Im3m) and qtz (P62 22) – have much higher symmetries and the smallest transitivities (12).
8). Some other relations are given in Ref. . 4) Ring nets. A natural application of ring nets is the description of topology of coordination polymers with synthons. The ring net describing synthons is partial, as a rule . 9). This means that the synthons in the lvt net can arrange in a diamondoid motif. In turn, the lvt topology describes a partial ring net for the gis atomic net, and so on. 3 Role of Geometrical and Coordination Parameters The criteria of high symmetry are not sufﬁcient to explain an important role of some ‘‘default’’ nets.
M. (2009) Topological relations between three-periodic nets. II. Binodal nets. , A65, 202–212. T. (2009) Three-dimensional Euclidean nets from two-dimensional hyperbolic tilings: kaleidoscopic examples. , A65, 81–108. A. (2006) A method for hierarchical comparative analysis of crystal structures. , A62, 356–364. M. (2000) Frameworks for extended solids: geometrical design principles. J. , 152, 3–20. , and Puschmann, 27 28 1 Periodic-Graph Approaches in Crystal Structure Prediction 46. 47. 48. 49.