Dodecahedra

CellgeometTy is governed predominantly by the final foam density and the external forces exerted on the cellular stmcture prior to its stabilization in the expanded state. In a foam prepared without such external forces, the cells tend to be spherical or ellipsoidal at gas volumes less than 70—80% of the total volume, and they tend toward the shape of packed regular dodecahedra at greater gas volumes. These shapes have been shown to be consistent with surface chemistry arguments (144,146,147). Photographs of actual foam cells (Fig. 2) show a broad range of variations in shape. 

The smaller cavities are distorted pentagon dodecahedra (distance of oxygen atoms to center varies between 3.77 and 3.95 A) their average free diameter is only about 5.0 A. The larger cavities are almost spherical the oxygen atoms lie at the vertices of hexadeca-hedra and their free diameter is 6.7 A. The distances have been calculated on the basis of a unit cell edge of 17.40 A as found for propane hydrate. 

Spot tests, 1, 552 Square antiprisms dodecahedra, cubes and, 1, 84 eight-coordinate compounds, 1,83 repulsion energy coefficients, 1, 33, 34 Square planar complexes, 1,191, 204 structure, 1, 37 Square pyramids five-coordinate compounds, 1,39 repulsion energy coefficients. 1,34 Squares... 

The oxygen atoms placed in the above positions form, in each unit cell, a framework consisting of two pentagonal dodecahedra, centered at... 

Dodecahedra of oxygen atoms at two corners and body center of unit cell, with three additional oxygen atoms (circles) needed to complete the structure. 

Fig. 1. The structure of gas hydrates containing a hydrogen-bonded framework of 46 water molecules. Twenty molecules, arranged at the comers of a pentagonal dodecahedron, form a hydrogen-bonded complex about the comers of the unit cube, and another 20 form a similar complex, differently oriented, about the centre of the cube. In addition there are six hydrogen-bonded water molecules, one of which is shown in the bottom face of the cube. In the proposed structure for water additional water molecules, not forming hydrogen bonds, occupy the centres of the dodecahedra, and...

It consists of discrete pentagonal dodecahedra each of which forms eight hydrogen bonds with eight surrounding dodecahedra. In addition, there are six water molecules in positions 0, etc., each of which forms four hydrogen bonds with molecules of the four surrounding dodecahedra in such a way that a complete tetrahedrally-bonded framework of 46 water molecules per unit cube is achieved. In this... 

The absence or very low intensity of 111, 311, 331, 333 and 511 indicates that clusters of atoms, perhaps 13-20, occupy the centres of the hexakaidecahedra, around iij and so on. There are also smaller clusters, probably of four atoms, inside the pentagonal dodecahedra, increasing the number of atoms in the 25.73-A cube to between 1,120 and 1,176. The composition of the alloys may be changed from MA16 by these additional atoms. 

With an increase in size of the active metals, the interlayer interstitials between the triacontahedral and the penultimate icosidodecahedral shells appear to be occupied by smaller electronegative components, with variable occupancies. These interlayer interstitials are actually the centers of cubes and correspond to the Wyckoff 8c (1/4 V4 A) special position in 1/1 ACs. Strictly speaking, occupation at this site means that the structure is no longer YCd6-type but, for convenience, they are still referred to as Tsai-type phases. According to Piao and coworkers [94], occupation of these cube centers has strong correlation with the orientations of the innermost tetrahedra and distortions of the dodecahedra. 

By using slightly different words, approximants are translationally normal crystal compounds generally with large unit cells that contain condensed, highly symmetric building blocks such as dodecahedra and icosahedra and have compositions close to those of related quasicrystals. 

Other coordination polyhedra based on bicapped dodecahedra, but having Dz symmetry, have been found for orthorhombic Phcn, Z =4) crystals of M(dip)2 (N03)3 (M=La, Tb and dip = 2,2 -dipyridyl) complexes (27(5, 277). Both La(III) and Tb(III) complexes have the same structure and this might be taken as evidence for the maintenance of the structure at least until Tb in the series. Sinha 218) have prepared the heavy lanthanide-bis-dipyridyl-trisnitrate complexes and the infrared studies 218, 219) showed no difference in the infrared spectra within the series, both ligands (dipyridyl and nitrate) being coordinated. 

---