Types Of Polyhedra Research Articles

Multiple empty tunnels in a new TaPS phase: Synthesis and structure determination of Ta 2P 2S 11

Ta 2P 2S 11 is a new phase of the TaPS system obtained by high-temperature synthesis from the elements. Single-crystal diffraction analysis showed the phase to crystallize in the P2 1 c space group with the following cell parameters: a = 6.876(3), Å, b = 24.109(8)Å, c = 26.411(8), Å, β = 106.04(3)°, V = 4208(6), Å 3, and Z = 10. Low-temperature ( T = 140 K) structure study has been performed and 3104 independent diffractometer data have been refined, with 328 variables, to R = 8.9%. The structure is made of two types of polyhedra, a tetrahedral group (PS 4) (mean d PS = 2.030, Å) and a bipolyhedral group (Ta 2S 11) (mean d TaS = 2.494, Å) in which tantalum is heptacoordinated. These (Ta 2S 11) units are formed of two distorted (TaS 7) groups sharing a triangular face made of mono- and disulfide anions ((S 2) −IIS −II). Of the three kinds of (Ta 2S 11) bipolyhedra, two of them show disorder of the common triangular sulfur face. The way the coordination groups are bonded to one another determines the occurrence of three kinds of tunnels in the structure. Their characteristics and the reason of their emptiness are related to their size and to the special linking arrangement taking place between the (PS 4) and (Ta 2S 11) groups. With the formulation Ta V 2P V 2(S 2) −II(S −II) 9 the phase is expected to be diamagnetic and semiconducting or insulator.

A new ordered sold solution with a bixbyite structure: The compounds Cu 2+xTi 2−xFe 2−xSb xO 9 (0 ⩽ x ⩽ 1.4)

A new solid solution with the formula Cu 2+xTi 2−xFe 2−xSb xO 9 was prepared by solid state reaction in air at 900°C. A rather large homogeneity range is observed: 0 ⩽ x ⩽ 1.4. The X-ray powder diffraction shows a (Fe, Mn) 2O 3 bixbyite type structure with a cubic elementary cell. The a parameter increases with the Cu +2 amount. Two types of polyhedra are present with on ordered cationic distribution over them. Cu +2 exhibits a highly distorted octahedral coordination: PII sites and Sb +5 an almost regular one: PI sites. The octahedral distortion is discussed in terms of two parameters: the bond length deviation Δoct and the bond angle variance σ 2 oct. The stabilization of the bixbyite structure is well understood in the context of a strong correlation between Δoct of the PII polyhedra and σ 2oct of the PI polyhedra.

A dual for Descartes’ theorem on polyhedra

The theory of duality is well known as a useful tool in the study of convex three-dimensional polyhedra. For example, if we know the types of polyhedra that can be circumscribed about a sphere, duality provides an immediate answer to the question as to what types can be inscribed in a sphere. Theorems like Euler’s Theorem (V – E + F = 2 where V, E and F are the numbers of vertices, edges and faces of a convex polyhedron) are self-dual in the sense that duality simply interchanges the values of V and F.

シロモンヤガの核多角体病ウイルスおよびか粒病ウイルスとその形態

The larvae of the spotted cutworm collected from grass fields at the beginning and the end of winter season were reared on an artificial diet in the laboratory. The larvae which died in the course of rearing were microscopically examined. In April and May, 1983, the main causative agents of diseased larvae were identified as nuclear polyhedrosis and granulosis. Two different types of polyhedra were observed: one was tetragonal and the other was trigonal in shape. Alkaline-liberated virions were rod-shaped and measured 80-190×320-380nm in the tetragonal type and 95-165×345-385nm in the trigonal type. The occlusion bodies of GV were ellipsoidal and measured 0.2-0.3×0.4-0.6μm. Nucleocapsids of GV were slightly curved and measured 70-72×400-405nm.

Über Wirkungsbereichsteilungen von kubischer Symmetrie *

Abstract. Partitions of the three-dimensional space by Dirichlet domains with cubic symmetry have been studied and a method of their derivation is described. Detailed results are given for a section through a zone of high instability in the space group I4132-O8. 172 types of polyhedra could be found in this section and their three-dimensional fields of existence were determined. Two types of Dirichlet domains with 38 faces and 70 vertices were discovered. ct. Partitions of the three-dimensional space by Dirichlet domains with cubic symmetry have been studied and a method of their derivation is described. Detailed results are given for a section through a zone of high instability in the space group I4132-O8. 172 types of polyhedra could be found in this section and their three-dimensional fields of existence were determined. Two types of Dirichlet domains with 38 faces and 70 vertices were discovered.

Prediction of diffuse intensity surfaces in short-range-ordered ternary derivative structures based on SnS, NaCl, CsCl and other structures

The atom arrangement in ternary and quaternary ionic long-range-ordered derivative structures of ZnS, NaCI, CsCI and others is governed by a principle which is known as Pauling's electrostatic valence rule. This valence rule is actually part of a more general ordering principle for derivative structures, which is not restricted to ionic compounds and requires that the smallest building blocks of the structure (centred tetrahedra, octahedra or cubes) have as far as possible a composition identical with the overall composition of the compound. Depending on the type of polyhedron, this rule can be fulfilled only for a limited number of overall compositions. In this case it is possible to produce an analytical formulation of the general ordering principle giving relations amongst the Warren short-range-order parameters. Use of these relations in a structure-factor formula of the binary base structure permits the derivation of the general location (lines, planes or a general surface) of superstructure reflexions or diffuse intensity in reciprocal space for the cases of long-range order or short-range order respectively. With this method it is possible not only to explain the experimentally determined diffuse intensity shapes due to short-range order in NaCl-related structures, but also to predict the diffuse intensity shape for ZnS and CsCl-related structures and others for which no experimental data are yet available.

Sur le diborure et le tétraborure de magnésium. Considérations cristallochimiques sur les tétraborures

MgB 2 and MgB 4 have been prepared at high temperature in sealed molybdenum vessels from mixtures of the elements. The utilization of an excess of metal in the vessel generates a pressure of magnesium vapor which inhibits thermal decomposition of the compounds during the synthesis. The structure of MgB 4 has been established from single crystal data collected on an automatic diffractometer. MgB 4 is orthorhombic, space group Pnam with a = 5.464; b = 7.472; c = 4.428Å and Z = 4. The structure of MgB 4, is based on chains of boron pentagonal pyramids in which the averaged BB bond is 1.787 Å. Interchain BB bonds of 1.730 Å are responsible for the three-dimensional boron framework. The Mg atoms, located in tunnels, form zigzag chains. The structure of MgB 4 is compared to those of ThB 4 and CrB 4; it is concluded that the size of the metal atom plays an important role in the nature of the boron framework which exists. In MgB 4, the fundamental unit of the boron skeleton is a pentagonal pyramid; a new feature, in boron-rich borides where this type of coordination polyhedron was previously found only in B 12 icosahedra.

Cytoplasmic Polyhedrosis of the Fall Webworm, Hyphantria cunea DRURY : Lepidoptera : Arctiidae

A cytoplasmic-polyhedrosis virus was obtained from larvae of the fall webworm, Hyphantria cunea DRURY, which had infested plane-trees in the Tachikawa area, Tokyo, in 1966.Two types of polyhedra, one with nearly spherical and the other with tetragonal outlines were observed. The sizes of the polyhedra ranged from 1.2 μ to 3.9 μ in diameter and ultra-thin sections of the infected midgut showed the presence of spherical virus particles and polyhedra in the cytoplasm of the cylindrical cells. The virus particles were approximately 30 mμ to 65 mμ in diamter.The cytoplasmic-polyhedrosis virus of the fall webworm was not infectious to the silkworm, Bombyx mori, and the cabbage armyworm, Mamestra brassicae, but highly infectious to Spilosoma punctaria. The larvae of the fall webworm were susceptible to the cytoplasmic-polyhedrosis virus of the alfalfa caterpillar, colias eurytheme and the armyworm, Pseudaletia unipuncta.

New type of coordination polyhedron for rare earth elements. The structure of the acetylacetoniminate of tris(acetylacetonato)ytterbium

New type of coordination polyhedron for rare earth elements. The structure of the acetylacetoniminate of tris(acetylacetonato)ytterbium

Histopathology of the cabbage looper, Trichoplusia ni, infected with a nuclear polyhedrosis

The histopathology of a nuclear polyhedrosis of the cabbage looper, Trichoplusia ni, infected with four viral preparations was investigated. As previously reported, the nuclei of hypodermis, fat body, tracheal matrix, and blood cells of the cabbage looper showed signs of infection. Polyhedra were also observed in the sarcolemma, neurilemma of nerves, segmental ganglia, subesophageal ganglion, and brain (including some neurones of these nerve tissues), testicular sheath, wing buds, some parts of silk glands and Malpighian tubules, and in connective tissue surrounding the midgut. Infection of midgut epithelium was observed infrequently following treatment with any preparation. Although two types of polyhedra, small and large, predominated in all four virus materials, polyhedra of different grades in size, but always of the same size in the same nucleus, were also observed.

Inducement of cytoplasmic polyhedrosis by the intrahemocoelic injection of freed viral particles into the silkworm, Bombyx mori

Cytoplasmic polyhedrosis was induced 1 1 In this paper the words “induce” and “inducement” are used in the general sense of causing to bring about, and not in the sense of meaning the activation of an occult virus or the provoked transformation of a provirus into a virulent virus, as defined by Steinhaus and Martignoni (1967). by the intrahemocoelic injection of freed viral particles into the silkworm, Bombyx mori. Examination of tissues of the infected insects revealed that formation of the typical tetragonal type of polyhedron was restricted to the gut epithelial cells. The LD 50's obtained with preparations of whole intact polyhedra and freed viral particles injected per os and into the hemocoel are compared.

Studies of two strains of cytoplasmic-polyhedrosis virus

With the use of the double-shadowing technique, the shapes of the polyhedra of two cytoplasmic-polyhedrosis-virus strains of the silkworm, Bombyx mori, are shown to be icosahedron and hexahedron, respectively. Ultrathin sections of the infected midgut show the presence of free virus particles, polyhedra, and virogenic stromata in the cytoplasm of the epithelial cells. In rare cases, the nucleus contains one or two inclusions similar to the polyhedra in the cytoplasm. The two virus strains are equally transmissible to Malacosoma neustria testacea, and they retain their infectivity for the silkworm after passage through the Malacosoma larvae. The shape of a new type of cytoplasmic polyhedron has been investigated, and a hypothetical model of the polyhedron is presented.

On the number of certain types of polyhedra

On the number of certain types of polyhedra

On some types of polyhedra

On some types of polyhedra

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