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).