Tetrahedral group Tetrahedron

Disregarding the type of bond, the tetrahedral group [Si04] is usually represented in the conventional ways outlined in figure 5.3, with the oxygen atoms at the corners and silicon at the center of the tetrahedron, and the structure of sih-cates is normally described as a function of the relative arrangements of the... 

The most numerous and most important tetrahedral structures are those in which only vertices are shared. The sharing of faces of tetrahedral groups AX4 would result in very close approach of the A atoms (to 0-67 AX or OAl XX, where XX is the length of the tetrahedron edge) and a very small A-X-A angle (38° 56 for regular tetrahedra) and for these reasons need not be considered. 

The dihedral group is the symmetry group for an n-sided regular polygon. The cubic group includes the octahedral group that represents the symmetries of the octahedron and the tetrahedral group that represents the symmetries of the tetrahedron. 

A Example (A regular tetrahedron, the tetrahedral group) Consider CH, which we... 

The second structure consists of silica tetrahedrons. In the tetrahedron, the silicon atom is equidistant from the hydroxyls. The silica tetrahedral groups are arranged to form a hexagonal network, which is repeated from sheet to sheet. 

The structure established by Bradley [1940] is rather unusual. It is, in fact, constituted by layers of tetrahedrons forming an hexagonal aggregate and, contrarily to other clays, the tetrahedral groups are directed sometimes upward, sometimes downward, in relation to a plane ( trans position). 

In all the groups along the chain, the bond angle is fixed. It is determined by considering a carbon atom at the centre of a regular tetrahedron and the four covalent bonds are in the directions of the four comers of the tetrahedron. This sets the bond angle at 109° 28 as shown in Fig. A.4 and this is called the tetrahedral angle. 

The predominantly ionic alkali metal sulfides M2S (Li, Na, K, Rb, Cs) adopt the antifluorite structure (p. 118) in which each S atom is surrounded by a cube of 8 M and each M by a tetrahedron of S. The alkaline earth sulfides MS (Mg, Ca, Sr, Ba) adopt the NaCl-type 6 6 structure (p. 242) as do many other monosulfides of rather less basic metals (M = Pb, Mn, La, Ce, Pr, Nd, Sm, Eu, Tb, Ho, Th, U, Pu). However, many metals in the later transition element groups show substantial trends to increasing covalency leading either to lower coordination numbers or to layer-lattice structures. Thus MS (Be, Zn, Cd, Hg) adopt the 4 4 zinc blende structure (p. 1210) and ZnS, CdS and MnS also crystallize in the 4 4 wurtzite modification (p. 1210). In both of these structures both M and S are tetrahedrally coordinated, whereas PtS, which also has 4 4... 

B8C18 has a dodecahedral Bg c/o.vo-skclclon with 2n = 16 electrons. In this case, the Wade rule neither can be applied, nor can it be interpreted as an electron precise cluster nor as a cluster with 3c2e bonds. B4(BF2)6 has a tetrahedral B4 skeleton with a radially bonded BF2 ligand at each vertex, but it has two more BF2 groups bonded to two tetrahedron edges. In such cases the simple electron counting rules fail. 

The most common geometrical arrangement of metals in tetrametal clusters is the tetrahedron, a polyhedron which represents the simplest case of a 3-dimensional cluster. It is convenient to start the discussion by considering the basic structures of the dodecacarbonyls and then to consider the effects produced by increasing and decreasing the number of carbonyl groups around the tetrahedral unit of metals. 

---