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Готові списки джерел за темами / Simplex form of a polyhedron / Статті в журналах

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Статті в журналах з теми "Simplex form of a polyhedron"

Автор: Grafiati

Опубліковано: 28 травня 2022

Оновлено: 31 липня 2025

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1

Yemets, Oleg A., Alexandra O. Yemets, and Ivan M. Polyakov. "Optimization on Arrangements: the Simplex Form of Polyhedron of Arrangements." Journal of Automation and Information Sciences 49, no. 12 (2017): 14–28. http://dx.doi.org/10.1615/jautomatinfscien.v49.i12.20.

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2

LAFONT, JEAN-FRANÇOIS, BRUCE A. MAGURN, and IVONNE J. ORTIZ. "Lower algebraic K-theory of certain reflection groups." Mathematical Proceedings of the Cambridge Philosophical Society 148, no. 2 (2009): 193–226. http://dx.doi.org/10.1017/s0305004109990363.

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AbstractFor P ⊂ 3 a finite volume geodesic polyhedron, with the property that all interior angles between incident faces are of the form π/mij (mij ≥ 2 an integer), there is a naturally associated Coxeter group ΓP. Furthermore, this Coxeter group is a lattice inside the semi-simple Lie group O+(3, 1) = Isom(3), with fundamental domain the original polyhedron P. In this paper, we provide a procedure for computing the lower algebraic K-theory of the integral group ring of such groups ΓP in terms of the geometry of the polyhedron P. As an ingredient in the computation, we explicitly calculate the

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3

GITLIN, CAROLE, JOSEPH O’ROURKE, and VINITA SUBRAMANIAN. "ON RECONSTRUCTING POLYHEDRA FROM PARALLEL SLICES." International Journal of Computational Geometry & Applications 06, no. 01 (1996): 103–22. http://dx.doi.org/10.1142/s0218195996000071.

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The problem of reconstructing a three-dimensional object from parallel slices has application in computer vision and medicine. Here we explore a specific existence question: given two polygons in parallel planes, is it always possible to find a polyhedron that has those polygons as faces, and whose vertices are precisely the vertices of the two polygons? We answer this question in the negative by providing an example of two polygons that cannot be connected to form a simple polyhedron. One polygon is a triangle, the other a somewhat complicated shape with spiraling pockets.

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4

Naskręcki, Bartosz, Mariusz Jaskolski, and Zbigniew Dauter. "The Euler characteristic as a basis for teaching topology concepts to crystallographers." Journal of Applied Crystallography 55, no. 1 (2022): 154–67. http://dx.doi.org/10.1107/s160057672101205x.

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The simple Euler polyhedral formula, expressed as an alternating count of the bounding faces, edges and vertices of any polyhedron, V − E + F = 2, is a fundamental concept in several branches of mathematics. Obviously, it is important in geometry, but it is also well known in topology, where a similar telescoping sum is known as the Euler characteristic χ of any finite space. The value of χ can also be computed for the unit polyhedra (such as the unit cell, the asymmetric unit or Dirichlet domain) which build, in a symmetric fashion, the infinite crystal lattices in all space groups. In this a

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5

Gilodo, A. Y., V. P. Kovtun, A. N. Arsirii, and A. A. Angel. "EFFECTIVE STRUCTURE OF A WOODEN RESIDENTIAL BUILDING IN THE FORM OF A GEODESIC DOME WITH A UNIVERSAL CONNECTOR." Bulletin of Odessa State Academy of Civil Engineering and Architecture, no. 82 (March 4, 2021): 19–26. http://dx.doi.org/10.31650/2415-377x-2021-82-19-26.

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Abstract. Since the middle of the twentieth century, a new architectural solution has been spherical shells broken down into elements by geodesic lines – circles with radii equal to the radius of the sphere. A geodesic dome is a dome made of a spherical polyhedron with an optimally distributed arrangement of vertices and edges tending to a perfect sphere. Using the technical capabilities of computer design, digital models of the layout and calculation of geodesic domes became available. It is possible not only to calculate multi-mesh network layouts with high accuracy, but also to automate the

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6

Xiong, Youlun, Han Ding, and Michael Yu Wang. "Quantitative Analysis of Inner Force Distribution and Load Capacity of Grasps and Fixtures." Journal of Manufacturing Science and Engineering 124, no. 2 (2002): 444–55. http://dx.doi.org/10.1115/1.1459089.

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This paper focuses on a quantitative analysis for grasp planning and fixture design based on an analytical description of point contact restraint. In the framework, the analysis deals with the fundamental concepts of restraint cone, freedom cone, force-determinacy and relative form closure. A method is presented to quantify the performance of a fixture (or grasp) with two major characteristics of inner force distribution and load capacity. Two different fixturing (or grasp) models of simplex grasp and elastic grasp are presented. It is shown that the performance of these two types of grasp (or

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7

Vovk, O. P., I. M. Naumko, and V. I. Pavlyshyn. "GENETIC SIGNIFICANCE OF VARIATIONS IN THE FACES OF THE SIMPLE FORMS OF TOPAZ CRYSTAL FROM CHAMBER PEGMATITES OF THE KOROSTEN PLUTON (UKRAINIAN SHIELD)." Mineralogical Journal 44, no. 3 (2022): 40–47. http://dx.doi.org/10.15407/mineraljournal.44.03.040.

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Topaz crystal morphology and habit distortion has been studied in various mineral-structural zones of chamber pegmatites of the Korosten pluton, which is located in north-western part of the Ukrainian Shield. It was assumed that the symmetry of the crystals obey the Curie principle. This means that only the symmetry elements common to the crystal and the medium in which it is formed will remain on real polyhedrons. The types of symmetry that contain the axes of infinite order are reduced to the following groups: 1) ∞L∞∞PC is a ball; 2) ∞L∞ is a ball filled with an optically active liquid; 3) L

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8

Newcomb, William W., Benes L. Trus, Naiqian Cheng, et al. "Isolation of Herpes Simplex Virus Procapsids from Cells Infected with a Protease-Deficient Mutant Virus." Journal of Virology 74, no. 4 (2000): 1663–73. http://dx.doi.org/10.1128/jvi.74.4.1663-1673.2000.

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ABSTRACT Herpes simplex virus type 1 (HSV-1) capsid proteins assemble in vitro into spherical procapsids that differ markedly in structure and stability from mature polyhedral capsids but can be converted to the mature form. Circumstantial evidence suggests that assembly in vivo follows a similar pathway of procapsid assembly and maturation, a pathway that resembles those of double-stranded DNA bacteriophages. We have confirmed the above pathway by isolating procapsids from HSV-1-infected cells and characterizing their morphology, thermal sensitivity, and protein composition. Experiments were

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9

Dasgupta, Anindya, and Duncan W. Wilson. "ATP Depletion Blocks Herpes Simplex Virus DNA Packaging and Capsid Maturation." Journal of Virology 73, no. 3 (1999): 2006–15. http://dx.doi.org/10.1128/jvi.73.3.2006-2015.1999.

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ABSTRACT During herpes simplex virus (HSV) assembly, immature procapsids must expel their internal scaffold proteins, transform their outer shell to form mature polyhedrons, and become packaged with the viral double-stranded (ds) DNA genome. A large number of virally encoded proteins are required for successful completion of these events, but their molecular roles are poorly understood. By analogy with the dsDNA bacteriophage we reasoned that HSV DNA packaging might be an ATP-requiring process and tested this hypothesis by adding an ATP depletion cocktail to cells accumulating unpackaged proca

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10

XU, HUIZHONG, YAPING WANG, DAJI LI, JIANYUAN XU, ZHUO WANG, and LIANG ZHEN. "STUDY OF THE NON-NBT PHASE IN Sr DOPED NBT THIN FILMS." Surface Review and Letters 20, no. 06 (2013): 1350056. http://dx.doi.org/10.1142/s0218625x1350056x.

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The morphology, composition and mechanism of the non-NBT phase in the Sr -doped NBT [SNBT, ( Na 0.5 Bi 0.5)1-x Sr x TiO 3] thin films by chemical method were investigated using XRD, SEM, crystallization analysis and thermodynamics analysis. The results showed that the non-NBT phase is the porphyroblastic grains in the matrix and looks like a plate-shaped polyhedron. The mechanism of the non-NBT phase formation is that the Sr 2+ and Na + combined with [Formula: see text] to form initial simple titanate, such as SrTiO 3, Na 2 TiO 3, or NBT phase decomposed because of the volatilization of Bi und

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11

Makri, Nancy. "Topological aspects of system-bath Hamiltonians and a vector model for multisite systems coupled to local, correlated, or common baths." Journal of Chemical Physics 158, no. 14 (2023): 144107. http://dx.doi.org/10.1063/5.0147135.

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Some topological features of multisite Hamiltonians consisting of harmonic potential surfaces with constant site-to-site couplings are discussed. Even in the absence of Duschinsky rotation, such a Hamiltonian assumes the system-bath form only if severe constraints exist. The simplest case of a common bath that couples to all sites is realized when the potential minima are collinear. The bath reorganization energy increases quadratically with site distance in this case. Another frequently encountered situation involves exciton-vibration coupling in molecular aggregates, where the intramolecular

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12

Le-Thi-Thu, Nga, Khoi Nguyen-Tan, and Thuy Nguyen-Thanh. "Reconstruction of Low Degree B-spline Surfaces with Arbitrary Topology Using Inverse Subdivision Scheme." Journal of Science and Technology: Issue on Information and Communications Technology 3, no. 1 (2017): 82. http://dx.doi.org/10.31130/jst.2017.41.

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Multivariate B-spline surfaces over triangular parametric domain have many interesting properties in the construction of smooth free-form surfaces. This paper introduces a novel approach to reconstruct triangular B-splines from a set of data points using inverse subdivision scheme. Our proposed method consists of two major steps. First, a control polyhedron of the triangular B-spline surface is created by applying the inverse subdivision scheme on an initial triangular mesh. Second, all control points of this B-spline surface, as well as knotclouds of its parametric domain are iteratively adju

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13

Hall, John, Lakin Wecker, Benjamin Ulmer, and Faramarz Samavati. "Disdyakis Triacontahedron DGGS." ISPRS International Journal of Geo-Information 9, no. 5 (2020): 315. http://dx.doi.org/10.3390/ijgi9050315.

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The amount of information collected about the Earth has become extremely large. With this information comes the demand for integration, processing, visualization and distribution of this data so that it can be leveraged to solve real-world problems. To address this issue, a carefully designed information structure is needed that stores all of the information about the Earth in a convenient format such that it can be easily used to solve a wide variety of problems. The idea which we explore is to create a Discrete Global Grid System (DGGS) using a Disdyakis Triacontahedron (DT) as the initial p

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14

Jiang, Yuhang, Shangke Jia, Shunwei Chen, Xuelian Li, Li Wang, and Xiujun Han. "Theoretical Prediction and Experimental Validation of the Glass-Forming Ability and Magnetic Properties of Fe-Si-B Metallic Glasses from Atomic Structures." Materials 15, no. 9 (2022): 3149. http://dx.doi.org/10.3390/ma15093149.

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Developing new soft magnetic amorphous alloys with a low cost and high saturation magnetization (Bs) in a simple alloy system has attracted substantial attention for industrialization and commercialization. Herein, the glass-forming ability (GFA), thermodynamic properties, soft magnetic properties, and atomic structures of Fe80+xSi5−xB15 (x = 0–4) amorphous soft magnetic alloys were investigated by ab initio molecular dynamics (AIMD) simulations and experiments. The pair distribution function (PDF), Voronoi polyhedron (VP), coordination number (CN), and chemical short- range order (CSRO) were

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15

Tang, Chengcheng, Xiang Sun, Alexandra Gomes, Johannes Wallner, and Helmut Pottmann. "Form-finding with polyhedral meshes made simple." ACM Transactions on Graphics 33, no. 4 (2014): 1–9. http://dx.doi.org/10.1145/2601097.2601213.

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16

Anochie, E. U., O. J. Jacob, E. M. Okoroafor, et al. "Linear Programming: Characteristics, Theory, Methods and Applications." Research Journal of Management Practice 4, no. 8 (2024): 13–21. https://doi.org/10.5281/zenodo.13912017.

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<em>Linear programming is a mathematical method that is used to determine the best possible outcome or solution from a given set of parameters or list of requirements, which are represented in the form of linear relationships. Characteristics of linear programming include constraints, objective’s function, linearity, finiteness, non- negativity, decision variables and data. The theory of linear programming is known as “The General representation Theorem” which will be clearly understood by taking note of the following definitions: “A hyper plane H in R ̃   is

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17

Minemyer, Barry. "Isometric embeddings of polyhedra into Euclidean space." Journal of Topology and Analysis 07, no. 04 (2015): 677–92. http://dx.doi.org/10.1142/s179352531550020x.

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In this paper we consider piecewise linear (pl) isometric embeddings of Euclidean polyhedra into Euclidean space. A Euclidean polyhedron is just a metric space [Formula: see text] which admits a triangulation [Formula: see text] such that each n-dimensional simplex of [Formula: see text] is affinely isometric to a simplex in 𝔼n. We prove that any 1-Lipschitz map from an n-dimensional Euclidean polyhedron [Formula: see text] into 𝔼3n is ϵ-close to a pl isometric embedding for any ϵ > 0. If we remove the condition that the map be pl, then any 1-Lipschitz map into 𝔼2n + 1 can be approximated b

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18

Nevskii, Mikhail V. "Estimation of interpolation projectors using Legendre polynomials." Modeling and Analysis of Information Systems 31, no. 3 (2024): 316–37. http://dx.doi.org/10.18255/1818-1015-2024-3-316-337.

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We give some estimates for the minimum projector norm under linear interpolation on a compact set in ${\mathbb R}^n$. Let $\Pi_1({\mathbb R}^n)$ be the space of polynomials in $n$ variables of degree at most $1$, $\Omega$ is a compactum in ${\mathbb R}^n$, $K={\rm conv}(\Omega)$. We will assume that ${\rm vol}(K)>0$. Let the points $x^{(j)}\in \Omega$, $1\leq j\leq n+1,$ be the vertices of an $n$-dimensional nondegenerate simplex. The interpolation projector $P:C(\Omega)\to \Pi_1({\mathbb R}^n)$ with the nodes $x^{(j)}$ is defined by the equations $Pf\left(x^{(j)}\right)=f\left(x^{(j)}\righ

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19

Azahroh, Inanda Shofa, and Fitria Zana Kumala. "Comparison of Students' Mathematical Concept Understanding Ability in Polyhedron Material Using the Discovery Learning and Core Learning Model with The Assistance of Pop-Up Book Media." Jurnal Pendidikan Matematika (JPM) 10, no. 1 (2024): 22–32. http://dx.doi.org/10.33474/jpm.v10i1.20359.

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This research was motivated by the low ability of class VIII students at MTs N 1 Purbalingga to understand mathematical concepts. This research aims to compare students' ability to understand mathematical concepts in flat-sided geometric material using two different learning models, namely discovery learning and Connecting, Organizing, Reflecting, And Extending (CORE) with the help of pop-up book media. The research method used is quantitative with a quasi-experimental type of research. The population in this study were class VIII students at MTs N 1 Purbalingga for the 2022/2023 academic year

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20

LEMMENS, BAS, and CORMAC WALSH. "ISOMETRIES OF POLYHEDRAL HILBERT GEOMETRIES." Journal of Topology and Analysis 03, no. 02 (2011): 213–41. http://dx.doi.org/10.1142/s1793525311000520.

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We show that the isometry group of a polyhedral Hilbert geometry coincides with its group of collineations (projectivities) if and only if the polyhedron is not an n-simplex with n ≥ 2. Moreover, we determine the isometry group of the Hilbert geometry on the n-simplex for all n ≥ 2, and find that it has the collineation group as an index-two subgroup. The results confirm several conjectures of P. de la Harpe for the class of polyhedral Hilbert geometries.

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21

Iemets, Oleg A., and Mariya V. Leonova. "Simplex Shape of the General Permutable Polyhedron Specified by Irreducible System." Journal of Automation and Information Sciences 46, no. 2 (2014): 42–55. http://dx.doi.org/10.1615/jautomatinfscien.v46.i2.40.

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22

Slavicek, James M., Melissa J. Mercer, and Mary Ellen Kelly. "Identification of a baculovirus polyhedron formation mutant with a novel phenotype." Proceedings, annual meeting, Electron Microscopy Society of America 54 (August 11, 1996): 796–97. http://dx.doi.org/10.1017/s0424820100166440.

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Nucleopolyhedroviruses (NPV, family Baculoviridae) produce two morphological forms, a budded virus form and a viral form that is occluded into a paracrystalline protein matrix. This structure is termed a polyhedron and is composed primarily of the protein polyhedrin. Insects are infected by NPVs after ingestion of the polyhedron and release of the occluded virions through dissolution of the polyhedron in the alkaline environment of the insect midgut. Early after infection the budded virus form is produced. It buds through the plasma membrane and then infects other cells. Later in the infection

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23

A. Hopkins, Mark. "Polyhedra faster than spheres?" Engineering Computations 31, no. 3 (2014): 567–83. http://dx.doi.org/10.1108/ec-09-2012-0211.

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Purpose – The purpose of this paper is to present a new and efficient technique for discrete element modelling using non-convex polyhedral grain shapes. Design/methodology/approach – The efficiency of the technique follows from the use of grains that are dilated versions of the basic polyhedral grain shapes. Dilation of an arbitrary polyhedral grain is accomplished by placing the center of a sphere of fixed radius at every point on the surface. The dilated vertices become sphere segments and the edges become cylinder segments. The sharpness of the vertices and edges can be adjusted by varying

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24

Xu, Zhi Gang, Jin Wang, Zi Xang Li, Chun Po Sun, and Tao Tao Liu. "Research on Non-Manifold Polyhedron from Function-to-Form Mapping." Advanced Materials Research 709 (June 2013): 499–502. http://dx.doi.org/10.4028/www.scientific.net/amr.709.499.

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In this paper, a class of non-manifold polyhedron is introduced and researched from a decomposition and mapping model (D-M for short). Design computing from function-to-form mapping and shape decomposition etc is reported. Modelling of non-manifold polyhedron is the key issue to develop function to form mapping process; and research on function to form mapping could help to develop the creative computational design tools.

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25

Ramírez Leal, Andrés Leonardo, Oscar Yecid Buitrago Suescún, Rodrigo Alberto Britto Agudelo, and A. Fedossova. "A new algorithm for solving linear programming problems." Ingeniería e Investigación 32, no. 2 (2012): 68–73. http://dx.doi.org/10.15446/ing.investig.v32n2.31949.

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Linear programming (LP) is one of the most widely-applied techniques in operations research. Many methods have been developed and several others are being proposed for solving LP problems, including the famous simplex method and interior point algorithms. This study was aimed at introducing a new method for solving LP problems. The proposed algorithm starts from an interior point and then carries out orthogonal projections using parametric straight lines to move between the interior and polyhedron frontier defining the feasible region until reaching the extreme optimal point.

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26

A.I., Eshniyоzov, and T.A.Iskandarova. "MODELS DESCRIBED BY BISTOCHASTIC QUADRATIC OPERATORS." JOURNAL OF NEW CENTURY INNOVATIONS 2, no. 1 (2022): 155–65. https://doi.org/10.5281/zenodo.6419009.

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Abstract:   The article introduces the concept of a bistochastic quadratic operator acting in  the  simplex  1 n S  .  Necessary  and  sufficient  conditions  for  bistochasticity  are  obtained. It is noticed that the set of all bistochastic quadratic operators acting in  1 n S ,  forms  a  polyhedron.  The  dynamical  and  statistical  (ergodic)  properties  of  the  trajectories of bistochastic quadratic operators are investigated. 

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27

Florian, Blachere, and Borouchaki Houman. "Covariance edges matrix of geometric elements." Annals of Mathematics and Physics 6, no. 2 (2023): 100–107. http://dx.doi.org/10.17352/amp.000088.

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In this paper, we introduce a new matrix associated with polygons and polyhedrons, namely the covariance edges matrix. We show that, for a regular polygon or polyhedron the corresponding matrix is proportional to the identity of size two or three. Based on this fact, we propose, as an application, several algebraic shape quality measures for convex polygons or polyhedrons. Furthermore, this matrix may be related to the metric of a simplex. Future studies will be devoted to the definition of the covariance edges matrix for higher elements and real applications to mesh optimisation.

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28

Bahri, Anthony, Soumen Sarkar, and Jongbaek Song. "Infinite families of equivariantly formal toric orbifolds." Forum Mathematicum 31, no. 2 (2019): 283–301. http://dx.doi.org/10.1515/forum-2018-0019.

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AbstractThe simplicial wedge construction on simplicial complexes and simple polytopes has been used by a variety of authors to study toric and related spaces, including non-singular toric varieties, toric manifolds, intersections of quadrics and more generally, polyhedral products. In this paper we extend the analysis to include toric orbifolds. Our main results yield infinite families of toric orbifolds, derived from a given one, whose integral cohomology is free of torsion and is concentrated in even degrees, a property which might be termed integrally equivariantly formal. In all cases, it

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29

Tevyashev, Andriy, Oleksii Haluza, Dmytro Kostaryev, Anton Paramonov, and Nataliia Sizova. "Devising a numerical method for estimating the positioning accuracy of aircraft by an information- communication network of optoelectronic stations." Eastern-European Journal of Enterprise Technologies 3, no. 9 (135) (2025): 101–20. https://doi.org/10.15587/1729-4061.2025.330922.

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The object of this study is the accuracy of aircraft positioning for open and covert video surveillance by an infocommunication network of optical-electronic stations along the trajectories of their movement. The task addressed is numerical assessment of the accuracy of aircraft positioning in airspace. It is proposed to use a convex polyhedron as a universal assessment of the accuracy of aircraft positioning, in which, with a given probability, the aircraft is located. It is shown that the lower estimate of this probability depends on the a priori information on the statistical properties of

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30

COLLARD, JEAN-FRANÇOIS, TANGUY RISSET, and PAUL FEAUTRIER. "CONSTRUCTION OF DO LOOPS FROM SYSTEMS OF AFFINE CONSTRAINTS." Parallel Processing Letters 05, no. 03 (1995): 421–36. http://dx.doi.org/10.1142/s0129626495000394.

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Most parallelization techniques for [Formula: see text] loop nests are based on reindexation. Reindexation yields a new iteration space, which is a convex integer polyhedron defined by a set of affine constraints. Parallel code generation thus needs to scan all the integer points of this convex, thereby requiring the construction of a new [Formula: see text] loop nest. We detail an algorithm to this purpose, which relies on a parametrized version of the Dual Simplex. We show how the resulting loop nest and especially the loop bounds can be kept simple, thus reducing the control overhead of par

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31

Lalik, Erwin. "Shannon information as a measure of distortion in coordination polyhedra." Journal of Applied Crystallography 38, no. 1 (2005): 152–57. http://dx.doi.org/10.1107/s0021889804030638.

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Variations in the distribution of bond orders within coordination polyhedra in crystals have been used as a scale of departure from perfect polyhedral symmetry and a measure of polyhedral distortion. The distribution of bond orders mathematically resembles the probability distribution; the bond orders can be normalized to their sum within a polyhedron and used to calculate the Shannon information content that depends on the degree of their departure from uniform distribution. The difference in the Shannon information between a perfect and a distorted polyhedron can be defined as a function tak

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32

Marshall, Kayleigh L., Jennifer A. Armstrong, and Mark T. Weller. "Gallium fluoroarsenates." Dalton Transactions 44, no. 28 (2015): 12804–11. http://dx.doi.org/10.1039/c5dt01094b.

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Анотація:

Gallium fluoroarsenates, templated with simple metal or complex organic cations, form structures derived from octahedrally coordinated gallium and AsO<sub>4</sub> tetrahedra, and displaying various polyhedra-linking dimensionalities.

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33

Sabitov, D. I., and I. Kh Sabitov. "Volume Polynomials for Some Polyhedra in Spaces of Constant Curvature." Modeling and Analysis of Information Systems 19, no. 6 (2015): 161–69. http://dx.doi.org/10.18255/1818-1015-2012-6-161-169.

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It is known that for each simplicial polyhedron P in 3-space there exists a monic polynomial Q depending on the combinatorial structure of P and the lengths of its edges only such that the volume of the polyhedron P as well as one of any polyhedron isometric to P and with the same combinatorial structure are roots of the polynomial Q. But this polynomial contains many millions of terms and it cannot be presented in an explicit form. In this work we indicate some special classes of polyhedra for which these polynomials can be found by a sufficiently effective algorithm which also works in space

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34

Woidy, Patrick, and Florian Kraus. "Crystal structure of Cs2[Th(NO3)6]." Acta Crystallographica Section E Structure Reports Online 70, no. 8 (2014): 98–100. http://dx.doi.org/10.1107/s1600536814015876.

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Dicaesium hexanitratothorate(IV), Cs2[Th(NO3)6], was synthesized in the form of colourless crystals by reaction of thorium nitrate and caesium nitrate in aqueous solution. The Th atom is located on an inversion centre and is coordinated by six chelating nitrate anions. The resulting ThO12coordination polyhedron is best described as a slightly distorted icosahedron. The Cs atom also has a coordination number of 12, but its coordination polyhedron is considerably more distorted. The crystal packing can be derived from an hexagonal dense packing (hcp) of idealized spherical CsO12and ThO12units. T

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35

Stefanides, Panagiotis. "Panagiotis Chr.Stefanides Invited to 4th TECHNIUM International Conference - Recognition of career." Technium: Romanian Journal of Applied Sciences and Technology 2, no. 3 (2020): 1–16. http://dx.doi.org/10.47577/technium.v2i3.454.

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As I anticipate, it concerns another genus of Polyhedron, a very Special one Ontologically, and this is very important Ι understand: “....Στερεὰ δὲ σώματα λέγεσθαι χρὴ …. πέντε, ……., τὸ δὲ ἄλλο γένος ἅπαν ἔχει μορφὴν μίαν·…..…ψυχῆς γένος"  http://remacle.org/bloodwolf/philosophes/platon/cousin/epinomisgrec.htm [..there are .. five solid bodies…. the other genus which in total has one form …the genus of the soul…] Plato’s Epinomis 981b. In 981a, of this work, Plato states that the composition of, soul and body bares a single form. Similarly, Plato in Timaeus [53 E] refer

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36

Wuttke, Joachim. "Numerically stable form factor of any polygon and polyhedron." Journal of Applied Crystallography 54, no. 2 (2021): 580–87. http://dx.doi.org/10.1107/s1600576721001710.

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Анотація:

Coordinate-free expressions for the form factors of arbitrary polygons and polyhedra are derived using the divergence theorem and Stokes's theorem. Apparent singularities, all removable, are discussed in detail. Cancellation near the singularities causes a loss of precision that can be avoided by using series expansions. An important application domain is small-angle scattering by nanocrystals.

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37

Romanova, Viktoryna A. "Vizualizing of semi-regular polyhedrons in AutoCAD environment." Structural Mechanics of Engineering Constructions and Buildings 15, no. 6 (2019): 449–57. http://dx.doi.org/10.22363/1815-5235-2019-15-6-449-457.

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The paper examines the automated formation by the kinematic method of the surfaces of Archimedes' semi-regular polyhedra of three forms: truncated tetrahedron, truncated octahedron and truncated icosahedron. To solve this problem, AutoCAD and the built-in programming language AutoLISP were used. Each of these five semi-regular polyhedra of Archimedes has faces of two kinds. In this regard, the surface of a separate polyhedron is considered to consist of two structural forms. Each structural shape is formed in the AutoCAD environment from the compartments of the surfaces of the faces of the pol

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38

Li, Xiu-Cai, Heng-Qiang Zhang, Qiong Yang, and Qi-Ying Zhang. "Synthesis and crystal structure of the two-dimensional coordination compound potassium oxo-bis(hydroxylamido)-pyridine-2, 3-dicarboxylato-vanadate(V)." Zeitschrift für Naturforschung B 70, no. 6 (2015): 373–77. http://dx.doi.org/10.1515/znb-2014-0244.

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Abstract:The crystal structure of the title compound, K2[VO(C7H3O4N)(NH2O)2(H2O)]2, is composed of KO9 and VO5N2 polyhedra connected through pyridine-2,3-dicarboxylate (2,3-dipicolinate) bridges. The VO5N2 coordination polyhedron is a pentagonal bipyramid, with hydroxylamido and dipicolinato ligands being bidentate. The axial positions are occupied by the terminal oxo ligand and one oxygen atom from a deprotonated carboxylate group. The oxygen atoms from hydroxylamido and the nitrogen atoms belonging either to the pyridine ring or to the hydroxylamido occupy the equatorial positions and form a

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39

Gosselin, C. M., and D. Gagnon-Lachance. "Expandable Polyhedral Mechanisms Based on Polygonal One-Degree-of-Freedom Faces." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 220, no. 7 (2006): 1011–18. http://dx.doi.org/10.1243/09544062jmes174.

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In this article, a new family of expandable mechanisms is presented. The proposed mechanisms are expandable polyhedra built using one-degree-of-freedom (one-DOF) planar linkages. The latter planar linkages have the shape of polygons and can be expanded while preserving their shape in any of their configurations. The planar mechanisms are used to form the faces of a polyhedron. They are assembled using spherical joints at the vertices of the polyhedron. The result is a one-DOF movable polyhedron which can be expanded while preserving its shape. The application of the principle on regular polyhe

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40

Elugachev, P. A., E. A. Esharov, B. M. Shumilov, and A. Zh Kuduev. "3D modeling of box-section road surface." Vestnik Tomskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. JOURNAL of Construction and Architecture 23, no. 1 (2021): 175–83. http://dx.doi.org/10.31675/1607-1859-2021-23-1-175-183.

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In road design, it is most important to obtain an optimum road surface (left and right traffic ways, left and right road sides, left and right slopes, etc.) using a number of criteria (sometimes hundreds of criteria), which include a slope, absolute elevation, elevation relative to the groundwater level, distance from the top of pipe-culvert, and others. In most computer-aided design systems, a digital model of the project is built by using a Delone triangulation.This paper deals with a new mathematical apparatus for spatial setting out of box-section roads in the form of a nonclosed polyhedro

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41

Hansen, R. O., and Xiaomu Wang. "Simplified frequency‐domain expressions for potential fields of arbitrary three‐dimensional bodies." GEOPHYSICS 53, no. 3 (1988): 365–74. http://dx.doi.org/10.1190/1.1442470.

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Models based on homogeneous polyhedral bodies offer great flexibility in representing the potential fields of complex geologic sources. However, existing expressions for the gravity and magnetic fields of such bodies suffer from two disadvantages. First, the surface of the body must be specified as a set of triangular facets, which makes input to a modeling program rather awkward. Second, each facet of the body must be rotated into a special position, which generates substantial computational overhead and makes the analytic expressions difficult to interpret. In this paper, Pedersen’s Fourier

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42

Byzov, Denis, and Petr Martyshko. "Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study." Mathematics 12, no. 6 (2024): 837. http://dx.doi.org/10.3390/math12060837.

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In this paper, the derivation of a concise closed form for the gravitational field of a polyhedron is presented. This formula forms the basis of the algorithm for calculating the gravitational field of an arbitrary shape body with high accuracy. Based on this algorithm, a method for gravity data inversion (creating density models of the Earth’s crust) has been developed. The algorithm can accept either regular or irregular polyhedron discretization for density model creation. The models are approximated with dense irregular grids, elements of which are polyhedrons. When performing gravity data

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43

Arai, Yoshihide, Takashi Sago, Yuki Ueyama, and Masanori Harada. "Quad-Rotor Avoidance Trajectory Generation for Convex Polyhedron Obstacles." Journal of Robotics and Mechatronics 36, no. 5 (2024): 1065–71. http://dx.doi.org/10.20965/jrm.2024.p1065.

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This study investigates a method for generating obstacle avoidance trajectories for arbitrary convex polyhedrons. We propose a formulation that converts discrete conditions into continuous equation forms to avoid convex polyhedron obstacles. The condition that the evaluation point be located outside of the convex polyhedron can be transformed into a constraint in the continuous equation form and incorporated into the optimization calculation to generate avoidance trajectories. Avoidance trajectory generation using the Legendre pseudospectral method is performed for convex polyhedral obstacles

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44

Wester, Ture. "3-D Form And Force Language Proposal For A Structural Basis." International Journal of Space Structures 11, no. 1-2 (1996): 221–31. http://dx.doi.org/10.1177/026635119601-227.

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Анотація:

The usually declared archetype for structural behaviour is the lattice (bar-and-node) structure. It is true that structural manifestations in general - with great clarity - may be reduced to the two interconnected structural nuclei, the pin-jointed bar and the hinged node. The relation to the geometrical archetypes, the five regular Platonic polyhedra, is obviously unsatisfactory, as only the three triangulated polyhedra have particular structural qualities in being kinematically stable. The two remaining, the cube and the dodecahedron, are unclear and usually considered as structurally inferi

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45

Kim, Eun-Kyoung. "The Acceptance patterns and meanings of polygonal bottle of the Qing Dynasty seen in Joseon white porcelain in the 19th century." Korean Journal of Art History 313 (March 31, 2022): 91–119. http://dx.doi.org/10.31065/kjah.313.202203.004.

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Анотація:

This polyhedron white porcelain, which suddenly appeared in the 19th century, is a new form that deviates from the tradition of making white porcelain in Joseon. This study paid attention to the emergence of polygonal bottle, which had not been independently viewed so far, and looked into the production aspects and formative characteristics along with the formative origins. Furthermore, the meaning of polygonal bottle consumed in the 19th century was examined. First, based on similar stylistically, it was revealed that the origin was a Glass-body painted enamel snuff bottle that was most likel

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46

Wei, Quanling, and Hong Yan. "A method of transferring polyhedron between the intersection-form and the sum-form." Computers & Mathematics with Applications 41, no. 10-11 (2001): 1327–42. http://dx.doi.org/10.1016/s0898-1221(01)00100-6.

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47

Kurir, Valerij. "Optimization the shape of the Francis hydraulic turbine." E3S Web of Conferences 220 (2020): 01067. http://dx.doi.org/10.1051/e3sconf/202022001067.

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The article presents one of the possible methods for optimizing the blade shape of a Francis radial-axial hydraulic turbine. The method for optimizing the shape of the turbine blade is based on the criterion of the maximum mechanical moment developed by the turbine. The blade shape optimization operation is conventionally divided into two stages. At the first stage of optimization of the blade shape, the analytical expression of the moment developed by the turbine is presented in a Taylor series by variable parameters − the coordinates of the vertices of the characteristic polyhedron of the me

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48

Abrosimov, Nikolay, and Bao Vuong. "The volume of a compact hyperbolic antiprism." Journal of Knot Theory and Its Ramifications 27, no. 13 (2018): 1842010. http://dx.doi.org/10.1142/s0218216518420105.

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Анотація:

We consider a compact hyperbolic antiprism. It is a convex polyhedron with [Formula: see text] vertices in the hyperbolic space [Formula: see text]. This polyhedron has a symmetry group [Formula: see text] generated by a mirror-rotational symmetry of order [Formula: see text], i.e. rotation to the angle [Formula: see text] followed by a reflection. We establish necessary and sufficient conditions for the existence of such polyhedra in [Formula: see text]. Then we find relations between their dihedral angles and edge lengths in the form of a cosine rule. Finally, we obtain exact integral formul

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49

Udovenko, Anatoly A., Arseny B. Slobodyuk, Tatiana B. Emelina, and Natalia M. Laptash. "Fluxional seven-coordinated fluorido- and oxofluoridotantalates." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 75, no. 6 (2019): 1115–25. http://dx.doi.org/10.1107/s2052520619013465.

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Seven-coordinated (NH4)2TaF7, Rb2TaF7 and Rb3TaOF6 were synthesized in single-crystal form and their structures were determined. A monocapped trigonal prism (CTP) or a pentagonal bipyramid (PB) of the TaF7 2− anion are stereochemically nonrigid and coexist in the first two compounds as a result of strong intraspheric dynamics. Upon cooling, tetragonal Rb2TaF7 undergoes a first-order phase transition at 145 K and the seven-coordinated polyhedron transforms into a regular CTP. The seven-coordinated polyhedron in (NH4)2TaF7 approaches the PB configuration as the temperature decreases. Cubic elpas

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50

Trishin, P. V. "Necessary and Sufficient Conditions for the Existence of Rational Solutions to Homogeneous Difference Equations with Constant Coefficients." Bulletin of Irkutsk State University. Series Mathematics 47 (2024): 47–62. http://dx.doi.org/10.26516/1997-7670.2024.47.47.

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A necessary and a sufficient condition for solvability of homogeneous difference equations with constant coefficients in the class of rational functions are obtained. The necessary condition is a restriction on the Newton polyhedron of the characteristic polynomial. In the two-dimensional case, this condition is the existence of parallel sides on the polygon. The sufficient condition is the equality to zero of certain sums of the coefficients of the equation. If the sufficient condition is satisfied, the solution is the class of rational functions whose denominators form a subring in the ring

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