Bond topology of chain, ribbon and tube silicates. Part II. Geometrical analysis of infinite 1D arrangements of (TO4)n− tetrahedra

Day, M.C.; Hawthorne, F.C.; Rostami, A.

doi:10.1107/S2053273324002432

Figure 14
(a) A unit-distance graph [isomorphic with the unit-distance graph in Fig. 13

(a)], the corresponding directed proto-graph, vertex subsets and the 3D modes. Mode (3) involves moving vertex 2 in 3D and may result in a geometrically identical (b) or distinct (c) planar unit-distance graph with respect to the original unit-distance graph in (a). Mode (4) involves moving vertices 1 and 2 in 3D as shown in (d) to produce a planar unit-distance graph that is geometrically identical to that shown in (a) and (b). Mode (4) may be applied to every second repeat unit as shown in (e) to produce a non-planar unit-distance graph that is geometrically distinct from the original unit-distance graph in (a). Mode (4) may also be applied by moving vertices 1 and 2 to symmetrically non-equivalent positions in each repeat unit as shown in (f) to produce an additional geometrically distinct non-planar unit-distance graph. Both 3D modes result in planar and non-planar unit-distance graphs that are geometrically distinct from the original unit-distance graph in (a) and are therefore valid. Blue 3D sheets show the geometry and orientation of each unit-distance graph. Legend as in Figs. 10

and 12

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ISSN: 2053-2733

Volume 80| Part 3| May 2024| Pages 258-281

https://doi.org/10.1107/S2053273324002432

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