Quadrilateral Faces Research Articles

Crystal and molecular structure of 2,2′-bipyridyldichloro(trimethyl)tantalum(V)

Crystals of the title compound are monoclinic, space group P21/m, a= 7·549(8), b= 12·422(12), c= 8·558(9)A, β= 109·7(2)°, Z= 2. The structure was solved from diffractometer data by Patterson and Fourier methods, and refined by least squares to R 0·08 for 762 independent reflections. A disordered structure model was refined space group P21/m. In each individual molecule, the tantalum atom has a distorted capped trigonal prismal environment, with one chlorine atom in the unique capping position [2·540(10)A]; the nitrogen atoms [2·291(21)A], one chlorine atom, and one methyl group form the capped quadrilateral face with two methyl groups [2·24(4) and 2·16(6)A] occupying the remaining edge. The molecule was refined with imposed m symmetry, so that the two sites in the quadrilateral face occupied by a chlorine atom and a methyl group were given equivalent mean scattering factors. The choice of geometry for this seven-co-ordinate (with five unidenta ligands) complex has been rationalised by considering the ligand–ligand repulsions and the constraints imposed by the bidentate 2,2′-bipyridyl ligand.

Crystal and molecular structure of dicarbonylchlorobis-[o-phenylene(dimethylarsino)]molybdenum(II) tri-iodide–bischloroform

Crystals of the title compound are orthorhombic, space group Pnma, with a= 11·75(1), b= 15·27(1), c= 24·15(2)A, Z= 4. The structure was solved by the heavy-atom method from 1048 independent reflections, collected by counter methods, and refined by full-matrix least-squares techniques to R 0·080. The symmetry of the cation is very close to C2v(mm) with one of the mirror planes imposed by the space group. Thus the molybdenum atom has a 1,4,2-capped trigonal prismatic environment with a chlorine atom in the unique capping position [2·575(11)A], four arsenic atoms in the capped quadrilateral face [2·614(5), 2·617(5)A], and two carbonyl groups making up the remaining edge [1·92(5), 1·87(5)A]. The tri-iodide ion lies with the central atom on a crystallographic mirror plane [2·903(2)A, 176·9(2)°].

Polyhedral Clathrate Hydrates. XIII. The Structure of (CH3CH2)2NH·8⅔H2O

A three-dimensional single crystal x-ray analysis of (CH3CH2)2NH·8⅔H2O has been carried out. The crystals are orthorhombic, with a=13.44 Å, b=11.77 Å, c=27.91 Å, and space group Pbcn. The compound is a clathrate hydrate, and the most notable feature of the water framework is a novel polyhedral cage, the 18-hedron (octakaidecahedron), which has twelve pentagonal and six hexagonal faces. The 18-hedra form a two-dimensional network by sharing faces. The networks are then linked together by additional water molecules in a manner which gives rise to additional ``irregular'' cages having quadrilateral, pentagonal, and hexagonal faces. Diethylamine molecules are enclosed in two types of cages and in both the amine groups are hydrogen bonded to the water lattice. In the case of the 18-hedra, this bonding somewhat distorts the cage from its ``ideal'' D3d shape. In marked contrast to previous clathrate structures involving polyhedra with pentagonal and hexagonal faces, where the dodecahedron could be considered to be the basic structural unit, the pentagonal dodecahedron does not appear in this structure.

POLYGONAL ASPECTS OF CELL FACES. II. QUADRILATERALS AS THE PREVAILING TYPE

Wheeler, George E. (Brooklyn Coll., Brooklyn, New York.) Polygonal aspects of cell faces. II. Quadrilaterals as the prevailing type. Amer. Jour. Bot. 49(4): 355–362. Illus. 1962.—Quadrilateral faces are abundant and even predominant among the faces of certain types of cells. Data taken from the literature and several original samples were studied to define the conditions which foster large numbers of quadrilaterals. The presence of free faces (cells on air spaces) profoundly affects cell‐face distributions. There is a great excess of quadrilaterals on cells with 2 free faces on opposite sides (cells of single layers). Among cells with 1 free face (cells of epidermises), pentagonal faces usually surpass quadrilateral faces, although they are just about equal in a few samples. Intermediate ratios of the 2 face types occur in samples which include cells having faces touching 1 free face, mixed with cells having faces between 2 free faces. The “competition” for numerical superiority shifts to pentagons vs. hexagons, among cells comprising internal tissues (cells in contact on all sides with other cells). With respect to epidermises, the relative size of epidermal and of subepidermal cells strongly influences the relative numbers of quadrilaterals and pentagons. A marked trend toward quadrilaterals may also be found in connection with a quite different set of cell relationships: if 2 layers of elongated cells occur together, and if their long axes are mutually perpendicular, then a “checkerboard” pattern may result. This arrangement favors large numbers of quadrilateral faces; in some samples, they may even dominate. It is suggested that certain modifications of this pattern may generate large numbers of triangular and of lenticular (lens‐shaped) faces. Varying patterns of cell division are considered to be primarily responsible for changes in cell‐face distributions and for changes in predominating face types.

AN APPROXIMATION OF THE MINIMAL TETRAKAIDECAHEDRON

THE ANALOGY between masses of cells and masses of bubbles has long fascinated students of cellular morphology. In fact, such basic researches on the nature of liquid films as those of Plateau (1873) had a profound effect on the development of modern studies of cell shapes. Kelvin's (1887) derivation of the mathematical concept of the minimal tetrakaidecahedron placed considerable emphasis on the stability of interfacial angles observed in soap films. Lewis (1923) adapted Kelvin's mathematical abstraction as an ideal cell shape. Although its actual realization among cells is a comparative rarity, the minimal tetrakaidecahedron continues to hold a focal point in cell-shape research. Since this report does not deal with cells directly the reader is referred to such papers as those by Meeuse (1942), Hulbary (1948), and Macior and Matzke (1951) for discussions of the occurrence of ideal configurations in masses of cells. In detailed comparisons of the shapes of cells and soap bubbles both Matzke (1945) and Lewis (1949) noted the absence of this geometrical form in masses of bubbles of uniform size. The 14-hedron is most commonly illustrated in the orthic form, fig. 1, which has straight edges and flat faces. The more precise minimal form, fig. 2, is technically difficult to illustrate, since the sides of the six quadrilateral faces are curved outwards while the eight hexagonal faces have undulating surfaces. Kelvin (1887) stated that he created a wire model of the minimal figure and succeeded in covering most of the surfaces with liquid films. Also, he was led to the postulation of this configuration by experiments with a cubical skeleton framework, originally devised by Plateau (1873). When this very instructive device is dipped into a soap solution and withdrawn, liquid films from each of the 12 edges extend toward the center of the frame. They do not, however, meet at a point. Instead, a flat-faced, quadrilateral film with outwardly curved edges is formed at the juncture. The films suspended from the framework form, in a sense, a portion of a minimal tetrakaidecahedron. As noted above, observations of these films provided the basic facts on which Kelvin based his ultimate derivation. As far as is known, no investigator has previously reported the creation of an entire minimal tetrakaidecahedron in soap films without the use of a

THE SHAPE OF COMPRESSED LEAD SHOT AND ITS RELATION TO CELL SHAPE

American Journal of BotanyVolume 26, Issue 5 p. 280-288 Article THE SHAPE OF COMPRESSED LEAD SHOT AND ITS RELATION TO CELL SHAPE James W. Marvin, James W. Marvin Department of Botany, Columbia University, New York CitySearch for more papers by this author James W. Marvin, James W. Marvin Department of Botany, Columbia University, New York CitySearch for more papers by this author First published: 01 May 1939 https://doi.org/10.1002/j.1537-2197.1939.tb09275.xCitations: 42AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume26, Issue5May 1939Pages 280-288 RelatedInformation