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Archimedean polyhedra as the basis of tetrahedrally-coordinated frameworks

Published online by Cambridge University Press:  14 March 2018

Paul B. Moore  and
Joseph V. Smith
Paul B. Moore
Affiliation:
Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois 37, U.S.A.
Joseph V. Smith
Affiliation:
Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois 37, U.S.A.
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Summary

The linkage of Archimedean polyhedra has been studied to provide trial models for tetrahedrally-coordinated structures such as zeolites. The cuboctahedron, rhombicuboctahedron, snub cube, icosidodecahedron, rhombicosidodecahedron, and snub dodecahedron cannot be used because four edges meet at a corner. The truncated tetrahedron, truncated cube, and truncated dodecahedron have triangular faces, and are unlikely to occur in silicate frameworks because of the instability of 3-rings. The truncated icosahedron and truncated icosidodecahedron have fivefold symmetry and cannot form four-connected frameworks with lattice symmetry. The truncated octahedron and truncated cuboctahedron may be linked either directly, in combination, or with square, hexagonal, or octagonal prisms. There are nine structures of which four are represented by sodalite, Linde A, faujasite, and ZK-5. The other five have the following properties: truncated octahedra linked H(H-S), Fd3m, a 17·5 Å; truncated octahedra linked H′(H-S) and (H-H), P63/mmc, a 12·4, c 20·5 Å; truncated octahedra linked H′(H-S) and (H-H), P63/mmc, a 17·5, c 28·5 Å; truncated cuboctahedra linked O′(S-S), Im3m, a 15·1 Å; truncated octahedra linked to truncated cuboctahedra H′(S-S), Fm3m, a 31·1 Å. The first symbol specifies the linking unit (H hexagon, H′ hexagonal prism, O′ octagonal prism) while the symbols in brackets specify the type of faces opposing across the contact (S square).

Type
Research Article
Information
Mineralogical magazine and journal of the Mineralogical Society , Volume 33 , Issue 266 , September 1964 , pp. 1008 - 1014
Copyright
Copyright © 1964, The Mineralogical Society

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