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All figures (14)
Figure 5 (Left) Twofold (3,5)-coordinated hms array (hms-c), (middle) the bouquet of the catenating rings of the two independent 6-rings (6a, 6b in red) with the HRN stars (yellow and green) and (right) a fragment of the corresponding (6,6)-coordinated binodal HRN.
Figure 6 Fragments of pcu-c, dia-c and srs-c arrays and the corresponding bouquets.
Figure 12 (Left) Self-catenated coesite (coe) network and the corresponding HRN; (right) bouquet and HRN star.
Figure 13 (Top) Self-catenated twt network and the corresponding HRN; (bottom) bouquets of catenating 12-rings and the corresponding HRN star. The catenated 12-ring is red, the four catenating 12-rings with numbers 1–4 are blue, and the HRN nodes (centres of 12-rings) are green.
Figure 1 Hopf, multiple crossing and the three simplest three-component links. The corresponding edges of the ring nets that connect the ring-net nodes are shown by arrows. For the Borromean link, the ring-net fragment contains an additional node in the centre of the link. The program Knotplot (R. G. Scharein; http://www.knotplot.com/) was used to draw the link pictures.
Figure 2 Two interpenetrating primitive cubic (pcu) networks (array pcu-c) shown in red and blue as well as the corresponding HRN of nbo (NbO) type highlighted in green. The bouquet of catenating rings and the corresponding HRN star (green balls) are shown in the second picture from the left.
Figure 8 Twofold arrays of square (sql) networks catenated in two different fashions: (top) square plane sql HRN in ACUCIK and (bottom) onedimensional zigzag HRN in YEVWIG. In both cases the bouquets of catenating 4-rings and the corresponding HRN stars are shown.
Figure 7 Two different views of the twofold dia array observed in LAYKOM: (a) shows seemingly regular adamantane-like fragments, but another view (b) makes distortion evident (see Fig. 6, dia-c, for comparison); there are two non-equivalent 6-rings (6a, 6b); (c), (d) and (e), (f) show the corresponding HRN stars and the bouquets that result in the two 6- coordinated (green) and 10-coordinated (yellow) HRN nodes. The corresponding 6,10-coordinated HRN is at the bottom.
Figure 3 Three equally catenated 14-rings in an interpenetrating array of two decorated diamondoid (dia-f) networks and the corresponding fragment of the simplified HRN. All the 14-rings are related via non-catenated 4-rings: 14a-ring = 14b-ring + 4-ring = 14c-ring + 4-ring + 4-ring (see text for details).
Figure 11 Parallel polycatenation in (top) GIMGIT and (bottom) BONNEY, BONNOI underlying nets and the corresponding HRNs, bouquets and HRN stars.
Figure 10 Inclined polycatenation in (top) ROZLIC, ROZLOI; (middle) COFNOB, COFNUH, COFPAP; (bottom) RONZOJ, RONZUP underlying nets and the corresponding HRNs, bouquets and HRN stars.
Figure 9 Inclined polycatenation of (left) hcb and (right) fes two-periodic networks and the corresponding one-dimensional linear chain HRNs. The 4-rings in fes do not participate in links and do not contribute to the HRN; their centres coincide with the centres of 8-rings of another fes network.
Table 1 Strong and essential rings in twofold interpenetrating arrays of some networks.
Figure 4 The bouquets of catenating rings in nine different network arrays that lead to the same star of simplified HRN of the nbo topology (cf. Fig. 2).
Journal Article
•
DOI
•
A topological method for the classification of entanglements in crystal networks
[...]
Eugeny V. Alexandrov
1
,
Vladislav A. Blatov
1
,
Davide M. Proserpio
2
•
Institutions (2)
Samara State University
1
,
University of Milan
2
01 Jul 2012
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Acta Crystallographica Section A