Face tetrahedra

Zhang, P, Ling, C. C., Coleman, A. W., Parrot-Lopez, H., and Galons, H. (1991), Formation of amphiphilic cyclodextrins via hydrophobic esterification at the secondary hydroxyl face, Tetrahedron Lett., 32, 2769-2770. 

The shape of polyhedra and the number of faces in them change continuously in the process of foam evolution (as a result of diffusion gas transfer and coalescence). Because of gas diffusion bubbles pass through transformation stages in which a body with five faces (pentahedron), then another body with four face (tetrahedron) [71] are formed and then they disappear. 

The symmetry of the structure we are looking for is imposed on the field 0(r) by building up the field inside a unit cubic cell of a smaller polyhedron, replicating it by reflections, translations, and rotations. Such a procedure not only guarantees that the field has the required symmetry but also enables substantial reduction of independent variables 0/ the function F (f)ij k )- For example, structures having the symmetry of the simple cubic phase are built of quadrirectangular tetrahedron replicated by reflection. The faces of the tetrahedron lie in the planes of mirror symmetry. The volume of the tetrahedron is 1 /48 of the unit cell volume. 

Vierfarbendruck, m. four-color printing. Vier-flach, n., -flachner, m. tetrahedron, vierflachig, a. fom-faced, tetrahedral. 

FIGURE 5.43 Hie zinc-blende (sphalerite) structure, rhe tour zinc ions (pink) form a tetrahedron within a face-centered cubic unit cell composed of sulfide ions (vellow).The zinc ions occupy half the tetrahedral holes between the sulfide ions, and the parts or the unit cell occupied by zinc ions are shaded blue. The detail shows how each zinc ion is surrounded by four sulfide ions each sulfide ion is similarly surrounded by four zinc ions. 

The arrangement of the centers of the molecules in the crystal is that corresponding to the diamond structure. Each molecule is surrounded tetrahedrally by four molecules. If we consider a molecule as roughly tetrahedral in shape with similar orientation to the tetrahedron formed by the four beryllium atoms, then the adjacent molecules are so oriented as to present tetrahedral faces to one another. 

Kang J, Kim TH, Yew KH, Lee WK (2003) The effect of face-blocking in the enantiose-lective aza-Claisen rearrangement of allylic imidates. Tetrahedron Asymmetry 14 415 18... 

The crystal structures of many organolithium compounds have been determined.44 Phenyllithium has been crystallized as an ether solvate. The structure is tetrameric with lithium and carbon atoms at alternating corners of a highly distorted cube. The lithium atoms form a tetrahedron and the carbons are associated with the faces of the tetrahedron. Each carbon is 2.33 A from the three neighboring lithium atoms and an ether molecule is coordinated to each lithium atom. Figures 7.2a and b show, respectively, the Li-C cluster and the complete array of atoms, except for hydrogen 45 Section 6.2 of Part A provides additional information on the structure of organolithium compounds. 

If there are not enough electrons for all of the polyhedron edges, 3c2e bonds on the triangular polyhedron faces can be the next best solution to compensate for the lack of electrons. This solution is only possible for deltahedra that have no more than four edges (and faces) meeting at any vertex. These include especially the tetrahedron, trigonal bipyramid and octahedron. 

For example, the bonding in B4C14 can be interpreted in the following way every boron atom takes part in four bonds, one 2c2e B-Cl bond and three 3c2< Cl bonds on the faces of the B4 tetrahedron. In this way every boron atom attains an electron octet. Eight of the valence electrons take part in the multicenter bonds the other eight are needed for the B-Cl bonds. 

FRANK-KASPER polyhedra in MgCu2. The polyhedron around an Mg atom (c.n. 16) is composed of 12 Cu atoms and of four Mg atoms that form a tetrahedron by themselves the Cu atoms form four triangles that are opposed to the Mg atoms. The polyhedron around a Cu atom (c.n. 12) is an icosahedron in which two opposite faces are occupied by Cu atoms... 

A polymeric structure is exhibited by "beryllium dimethyl," which is actually [Be(CH3)2] (see the structure of (BeCl2) shown earlier), and LiCH3 exists as a tetramer, (LiCH3)4. The structure of the tet-ramer involves a tetrahedron of Li atoms with a methyl group residing above each face of the tetrahedron. An orbital on the CH3 group forms multicentered bonds to four Li atoms. There are numerous compounds for which the electron-deficient nature of the molecules leads to aggregation. 

A great deal of effort has been directed to determining the structures of lithium alkyls. It has been determined that in hydrocarbon solutions the dominant species is a hexamer when the alkyl groups are small. In the solid phase, the structure is body-centered cubic with the (LiCH3)4 units at each lattice site. Each unit is a tetramer in which the four lithium atoms reside at the comers of a tetrahedron and the methyl groups are located above the centers of the triangular faces. The carbon atoms of... 

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