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

Acta Crystallographica Section A
Acta Crystallographica
Section A FOUNDATIONS AND ADVANCES

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Figure 13
(a) A unit-distance graph, the corresponding directed proto-graph, vertex subsets and the 2D modes. Mode (1) involves moving vertex 2 in 2D as shown in (b) to produce a planar unit-distance graph that is geometrically distinct from the original unit-distance graph in (a). Mode (2) involves moving vertices 1 and 2 in 2D as shown in (c) to produce a planar unit-distance graph that is geometrically identical to that shown in (b). Mode (2) may be applied to every second or third repeat unit as shown in (d) and (e), respectively, to produce two planar unit-distance graphs that are both geometrically distinct from the original unit-distance graph in (a). Mode (2) 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 planar unit-distance graph. Both 2D modes result in planar unit-distance graphs that are geometrically distinct from the original unit-distance graph in (a) and are therefore valid. Legend as in Figs. 10

and 12

FOUNDATIONS
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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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