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Journal articles on the topic 'Polyhedra'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Makovicky, E., and T. Balić-Žunić. "New Measure of Distortion for Coordination Polyhedra." Acta Crystallographica Section B Structural Science 54, no. 6 (1998): 766–73. http://dx.doi.org/10.1107/s0108768198003905.

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A new global measure of distortion for coordination polyhedra is proposed, based on a comparison of the ratios Vs (circumscribed sphere)/Vp (polyhedron) calculated, respectively, for the real and ideal polyhedra of the same number of coordinated atoms which have the same circumscribed sphere. This formula can be simplified to υ (%) = 100[Vi (ideal) − Vr (real)]/Vi , where Vi and Vr are the volumes of the above-defined polyhedra. The global distortion can be combined with other polyhedral characteristics, e.g. with the eccentricity of the central atom in the polyhedron or with the degree of sph

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2

Senesi, Andrew, and Byeongdu Lee. "Scattering functions of polyhedra." Journal of Applied Crystallography 48, no. 2 (2015): 565–77. http://dx.doi.org/10.1107/s1600576715002964.

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Herein, a general method to calculate the scattering functions of polyhedra, including both regular and semi-regular polyhedra, is presented. These calculations may be achieved by breaking a polyhedron into sets of congruent pieces, thereby reducing computation time by taking advantage of Fourier transforms and inversion symmetry. Each piece belonging to a set or subunit can be generated by either rotation or translation. Further, general strategies to compute truncated, concave and stellated polyhedra are provided. Using this method, the asymptotic behaviors of the polyhedral scattering funct

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3

Eason, Jane E., Robert H. Hice, Jeffrey J. Johnson, and Brian A. Federici. "Effects of Substituting Granulin or a Granulin-Polyhedrin Chimera for Polyhedrin on Virion Occlusion and Polyhedral Morphology in Autographa californicaMultinucleocapsid Nuclear Polyhedrosis Virus." Journal of Virology 72, no. 7 (1998): 6237–43. http://dx.doi.org/10.1128/jvi.72.7.6237-6243.1998.

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ABSTRACT Substitution of granulin from the Trichoplusia nigranulosis virus (TnGV) for polyhedrin of the Autographa californica multinucleocapsid nuclear polyhedrosis virus (AcMNPV) yielded a few very large (2 to 5 μm) cuboidal inclusions in the cytoplasm and nucleus of infected cells. These polyhedra lacked the beveled edges characteristic of wild-type AcMNPV polyhedra, contained fractures, and occluded few virions. Placing a nuclear localization signal (KRKK) in granulin directed more granulin to the nucleus and resulted in more structurally uniform cuboidal inclusions in which no virions wer

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4

Bokowski, Jürgen, and Kevin H. "Polyhedral Embeddings of Triangular Regular Maps of Genus g, 2 ⩽ g ⩽ 14, and Neighborly Spatial Polyhedra." Symmetry 17, no. 4 (2025): 622. https://doi.org/10.3390/sym17040622.

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This article provides a survey of polyhedral embeddings of triangular regular maps of genus g, 2⩽g⩽14, and of neighborly spatial polyhedra. An old conjecture of Grünbaum from 1967, although disproved in 2000, lies behind this investigation. We discuss all duals of these polyhedra as well, whereby we accept, e.g., the Szilassi torus with its non-convex faces to be a dual of the Möbius torus. A numerical optimization approach by the second author for finding such embeddings was first applied to finding (unsuccessfully) a dual polyhedron of one of the 59 closed oriented surfaces with the complete

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Koźniewski, Edwin. "Flat Tessellations in Search of a Dome Shape." Buildings 15, no. 3 (2025): 453. https://doi.org/10.3390/buildings15030453.

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Based on the design solutions of the Orthodox Church and while maintaining the conventions of polyhedral surfaces, the author describes and analyzes new 3D geometric solids (structures) modeled on tessellations. The pretext for undertaking the research was the need to find a polyhedron shape that could replace the curvilinear shape of a burning candle flame that had been used for centuries in Orthodox church architecture. The innovative idea of designing polyhedral domes of Orthodox churches led the designer to interesting structures that are not derived from either regular or semiregular poly

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Ju, Ming-Yi, Ming-Yi Ju, Jing-Sin Liu, et al. "Fast and accurate collision detection based on enclosed ellipsoid." Robotica 19, no. 4 (2001): 381–94. http://dx.doi.org/10.1017/s0263574700003295.

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A fast and accurate method for detecting the collisions of convex polyhedra in a graphical simulation environment based on a newly developed method of distance estimate is presented. By the simultaneous use of the enclosing and the enclosed ellipsoids of convex polyhedra, potential collisions can be detected more accurate than those methods using only bounding volume for object representation, and more efficient than the polyhedral methods. An approach for computing the enclosed ellipsoid of a convex polyhedron by compressing, stretching and scaling operations on its best-fit enclosing ellipso

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FEKETE, SÁNDOR P., and JOSEPH S. B. MITCHELL. "TERRAIN DECOMPOSITION AND LAYERED MANUFACTURING." International Journal of Computational Geometry & Applications 11, no. 06 (2001): 647–68. http://dx.doi.org/10.1142/s0218195901000687.

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We consider a problem that arises in generating three-dimensional models by methods of layered manufacturing: How does one decompose a given model P into a small number of sub-models each of which is a terrain polyhedron? Terrain polyhedra have a base facet such that, for each point of the polyhedron, the line segment joining the point to its orthogonal projection on the base facet lies within the polyhedron. Terrain polyhedra are exactly the class of polyhedral models for which it is possible to construct the model using layered manufacturing (with layers parallel to the base facet), without

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8

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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9

Chubanov, Sergei. "On the Complexity of PAC Learning in Hilbert Spaces." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 6 (2023): 7202–9. http://dx.doi.org/10.1609/aaai.v37i6.25878.

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We study the problem of binary classification from the point of view of learning convex polyhedra in Hilbert spaces, to which one can reduce any binary classification problem. The problem of learning convex polyhedra in finite-dimensional spaces is sufficiently well studied in the literature. We generalize this problem to that in a Hilbert space and propose an algorithm for learning a polyhedron which correctly classifies at least 1 − ε of the distribution, with a probability of at least 1 − δ, where ε and δ are given parameters. Also, as a corollary, we improve some previous bounds for polyhe

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Wecker, Lakin, John Hall, and Faramarz F. Samavati. "Constructing Efficient Mesh-Based Global Grid Systems with Reduced Distortions." ISPRS International Journal of Geo-Information 13, no. 11 (2024): 373. http://dx.doi.org/10.3390/ijgi13110373.

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Recent advancements in geospatial technologies have significantly expanded the volume and diversity of geospatial data, unlocking new and innovative applications that require novel Geographic Information Systems (GIS). (Discrete) Global Grid Systems (DGGSs) have emerged as a promising solution to further enhance modern geospatial capabilities. Current DGGSs employ a simple, low-resolution polyhedral approximation of the Earth for efficient operations, but require a projection between the Earth’s surface and the polyhedral faces. Equal-area DGGSs are desirable for their low distortion, but they

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11

Subbotin, Vladimir Ivanovich. "On the enumeration of convex 𝑅𝑅-polyhedra". Chebyshevskii Sbornik 24, № 5 (2024): 194–207. https://doi.org/10.22405/2226-8383-2023-24-5-194-207.

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The problem of enumerating a class of polyhedra with given symmetry conditions is one of the important problems of the modern theory of convex polyhedra. There are many works in which the problem of a complete enumeration of polyhedra with symmetry conditions is posed.If we limit ourselves to polyhedra in 𝐸3, then examples of such polyhedra are regular, regular stellate, Archimedean polyhedra, the Johnson-Zalgaller class, polyhedra with conditional edges, and polyhedra with parquet faces. Specifically, the symmetry conditions for the class of closed convex regular polyhedra consist in the cond

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12

Nozaki, H., and M. Taya. "Elastic Fields in a Polyhedral Inclusion With Uniform Eigenstrains and Related Problems." Journal of Applied Mechanics 68, no. 3 (2000): 441–52. http://dx.doi.org/10.1115/1.1362670.

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In this paper, the elastic field in an infinite elastic body containing a polyhedral inclusion with uniform eigenstrains is investigated. Exact solutions are obtained for the stress field in and around a fully general polyhedron, i.e., an arbitrary bounded region of three-dimensional space with a piecewise planner boundary. Numerical results are presented for the stress field and the strain energy for several major polyhedra and the effective stiffness of a composite with regular polyhedral inhomogeneities. It is found that the stresses at the center of a polyhedral inclusion with uniaxial eig

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13

Sundberg, Sue E. "A Plethora of Polyhedra." Mathematics Teaching in the Middle School 3, no. 6 (1998): 388–91. http://dx.doi.org/10.5951/mtms.3.6.0388.

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So, just what is a polyhedron? we could say that a polyhedron is a simple closed surface in space whose boundary is composed of polygonal regions, but most middle school students would not understand this definition. Instead, involving students in an activity in which they actually create polyhedra enable them to understand the characteristics of different polyhedra and develop a clear definition for themselves. Once students gain a hands-on understanding of polyhedra, the shapes can be used to reveal a plethora of other geometric concepts.

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14

Feng, Y. T., and Yuanqiang Tan. "On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra." Engineering Computations 37, no. 1 (2019): 54–72. http://dx.doi.org/10.1108/ec-03-2019-0124.

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Purpose Contact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called entrance block of two polyhedra and reduces the contact to evaluate the distance between the reference point to the corresponding entrance block, but effective implementation is still lacking. Design/methodology/approach In this paper, the equivalence of the entrance block and the Minkowski difference

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15

Caglayan, Günhan. "Hanging Around with Platonic Solids." Mathematics Teacher 112, no. 5 (2019): 328–29. http://dx.doi.org/10.5951/mathteacher.112.5.0328.

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The Platonic solids, also known as the five regular polyhedra, are the five solids whose faces are congruent regular polygons of the same type. Polyhedra is plural for polyhedron, derived from the Greek poly + hedros, meaning “multi-faces.” The five Platonic solids include the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. Photographs 1a-d show several regular polyhedra

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16

Erdanov, Panji Nuraliyevich. "MULTIFACETED STRUCTURES IN ARCHITECTURE." Modern Scientific Research International Scientific Journal 1, no. 7 (2023): 70–76. https://doi.org/10.5281/zenodo.10017345.

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The article analyzes the problems of using polyhedra and their modifications in architecture, construction and technology. Prisms, pyramids, prismatoids, Platonic and Archimedean solids, quasi-polyhedra and some figures composed on their basis, as well as polyhedral domes, umbrella shells and folds from flat fragments of the same type are considered.

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17

Lee, J., J. Duffy, and J. Rooney. "An initial investigation into the geometrical meaning of the (pseudo-) inverses of the line matrices for the edges of platonic polyhedra." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 216, no. 1 (2002): 25–30. http://dx.doi.org/10.1243/0954406021524882.

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It is well known that there are five regular (Platonic) polyhedra: the tetrahedron, the hexahedron (cube), the octahedron, the icosahedron and the dodecahedron. Each of these polyhedra has an associated dual polyhedron which is also Platonic. By considering the Platonic polyhedra to be constructed from lines, and then representing the lines in terms of both ray and axis coordinates, a further aspect of this duality is exposed. This is the duality of poles and polars associated with projective configurations of points, lines and planes. This paper shows that a line matrix may be constructed for

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18

Vologzhanina, A. V., D. V. Pushkin, and V. N. Serezhkin. "LnO n coordination polyhedra (Ln = La–Lu) in crystal structures." Acta Crystallographica Section B Structural Science 62, no. 5 (2006): 754–60. http://dx.doi.org/10.1107/s0108768106018726.

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Voronoi–Dirichlet (VD) polyhedra and the method of intersecting spheres were used to analyze the crystal structures of 2917 compounds containing 3903 crystallographically non-equivalent types of LnO n polyhedra (Ln = La–Lu). It was established that Ln coordination numbers (CN) vary from 3 to 12, and 20 types of coordination polyhedra are present in the structures. Despite the great diversity of CN and types of coordination polyhedra, the volume of the VD polyhedron was found to depend only on the identity of the Ln atom and its oxidation state.

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JIANG, BOJU, and SHICHENG WANG. "ACHIRALITY AND PLANARITY." Communications in Contemporary Mathematics 02, no. 03 (2000): 299–305. http://dx.doi.org/10.1142/s0219199700000141.

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An embedding of a space Y into the 3-sphere S3 is said to be strictly achiral if its image is pointwise fixed by an orientation reversing homeomorphism of S3. A space Y is said to be abstractly planar if it can be embedded into the 2-sphere S2. We first extend Kuratowski Theorem into a criterion for abstract planarity of polyhedra, then show that a polyhedron has a strictly achiral polyhedral embedding into S3 if and only if it is abstractly planar. Some related higher dimensional examples are also discussed.

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Radović, Ljiljana, Paulus Gerdes, Slavik Jablan, and Radmila Sazdanovic. "Plaited polyhedra: A knot theory point of view." Journal of Knot Theory and Its Ramifications 25, no. 09 (2016): 1641006. http://dx.doi.org/10.1142/s0218216516410066.

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Plaited polyhedra, discovered by P. Gerdes in African dance rattle capsules are analyzed from the knot-theory point of view. Every plaited polyhedron can be derived from a knot or link diagram as its dual. In the attempt to classify obtained plaited polyhedra, we propose different methods based on families of knots and links in Conway notation or their corresponding braid families, both leading to the notion of families of plaited polyhedra.

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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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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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Qousini, Maysoon, Hasan Hdieb, and Eman Almuhur. "Applications of Locally Compact Spaces in Polyhedra: Dimension and Limits." WSEAS TRANSACTIONS ON MATHEMATICS 23 (February 27, 2024): 118–24. http://dx.doi.org/10.37394/23206.2024.23.14.

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The study of applications of locally compact spaces in polyhedra in relation to their dimensions as well as homotopy and extension problems developed in the late 1940s and early 1950s under the leadership of mathematician. Many mathematicians studied application locally compact in polyhedra. A polyhedron can be obtained by subdivision, as a simplicial metric complex; thus, re-gluings of polyhedra can also be seen as simple complexes. Thus, the topology of a simplicial metric complex X is the topology quotient of the reattachment. The objective of this work is to shed light on the applications

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Rosa, M. E., and M. A. Fortes. "New types of space-filling polyhedra with fourteen faces." Acta Crystallographica Section A Foundations of Crystallography 42, no. 4 (1986): 282–86. http://dx.doi.org/10.1107/s0108767386099300.

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A study of the staggered packing of identical hexagonal prisms leading to four-connected periodic structures with polyhedral cells of fourteen faces has been undertaken. Special attention was given to those packings that lead to periodic structures with two polyhedra per lattice point, and such that the two polyhedra are related by a pure rotation and/or enantiomorphism. The general solution for packings of this type was obtained and the topology of the intervening polyhedra was determined. It is shown that polyhedra with eight hexagonal faces and six square faces, topologically isomorphic to

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Kampf, A. R., F. Colombo, and J. González del Tánago. "Carlhintzeite, Ca2AlF7·H2O, from the Gigante granitic pegmatite, Córdoba province, Argentina: description and crystal structure." Mineralogical Magazine 74, no. 4 (2010): 623–32. http://dx.doi.org/10.1180/minmag.2010.074.4.623.

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AbstractCarlhintzeite, Ca2AlF7·H2O, has been found at the Gigante pegmatite, Punilla Department, Córdoba Province, Argentina. It occurs as colourless prismatic crystals up to 0.8 mm long, ubiquitously twinned on {001}. Electron microprobe analyses provided the empirical formula Ca1.98Al1.02F6.24(OH)0.76·H1.62O. A crystal fragment used for the collection of structure data provided the triclinic, C1̄ cell: a = 9.4227(4), b = 6.9670(5), c = 9.2671(7) Å, α = 90.974(6), β = 104.802(5), γ = 90.026(6)°, V = 558.08(7) Å3 and Z = 4. The crystal structure, solved by direct methods and refined to R1 = 0.

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Schulte, E., and J. M. Wills. "Kepler-Poinsot-Type Realizations of Regular Maps of Klein, Fricke, Gordan and Sherk." Canadian Mathematical Bulletin 30, no. 2 (1987): 155–64. http://dx.doi.org/10.4153/cmb-1987-023-9.

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AbstractThe paper describes polyhedral realizations for Felix Klein's map {3, 7}8 of genus 3, for Gordan's map {4, 5}6 of genus 4, and for two maps of genus 5, the Klein-Fricke map of type {3, 8} and Sherk's map of type {4, 6}. The polyhedra have self-intersections but high symmetry and thus are close analogues to the Kepler-Poinsot-polyhedra.

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Li, Hongbo, Lina Zhao, and Ying Chen. "A symbolic approach to polyhedral scene analysis by parametric calotte propagation." Robotica 26, no. 4 (2008): 483–501. http://dx.doi.org/10.1017/s0263574707003918.

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SUMMARYPolyhedral scene analysis studies whether a 2D line drawing of a 3D polyhedron is realizable in space, and if so, it gives the results of parameterizing the space of all possible realizations. For generic 2D data, symbolic computation with Grassmann–Cayley algebra is needed in the analysis. In this paper, we propose a method called parametric calotte propagation to solve the realization and parameterization problems for general polyhedral scenes at the same time. In algebraic manipulation, parametric propagation is more efficient than elimination. In applications, it can lead to linear

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Mokhnacheva, A. A., K. V. Gerasimova, and D. N. Ibragimov. "Methods of Numerical Simulation of 0-Controllable Sets of a Linear Discrete Dynamical System with Limited Control Based on Polyhedral Approximation Algorithms." Моделирование и анализ данных 13, no. 4 (2023): 84–110. http://dx.doi.org/10.17759/mda.2023130405.

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<p>The article deals with the problem of constructing a polyhedral approximation of the 0-controllable sets of a linear discrete-time system with linear control constraints. To carry out the approximation, it is proposed to use two heuristic algorithms aimed at reducing the number of vertices of an arbitrary polyhedron while maintaining the accuracy of the description in the sense of the Hausdorff distance. The reduction of the problem of calculating the distance between nested polyhedra to the problem of convex programming is demonstrated. The issues of optimality of obtained approximat

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Krasnov, V. A. "Volumes of Polyhedra in Non-Euclidean Spaces of Constant Curvature." Contemporary Mathematics. Fundamental Directions 66, no. 4 (2020): 558–679. http://dx.doi.org/10.22363/2413-3639-2020-66-4-558-679.

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Computation of the volumes of polyhedra is a classical geometry problem known since ancient mathematics and preserving its importance until present time. Deriving volume formulas for 3-dimensional non-Euclidean polyhedra of a given combinatorial type is a very difficult problem. Nowadays, it is fully solved for a tetrahedron, the most simple polyhedron in the combinatorial sense. However, it is well known that for a polyhedron of a special type its volume formula becomes much simpler. This fact was noted by Lobachevsky who found the volume of the so-called ideal tetrahedron in hyperbolic space

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Siqueira, Paulo Henrique. "A virtual reality web environment create to visualize Archimedean Polyhedra and their Catalan duals." Revista de Ciencia y Tecnología, no. 41 (July 11, 2024): 76–82. https://doi.org/10.36995/j.recyt.2024.41.009.

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This paper shows the use of web resources to create environments for visualizing Archimedean polyhedra and the respective Catalan duals. These environments were created using Virtual Reality (VR) resources, which allow the visitor to manipulate the polyhedra and compare the polyhedra and their duals. Geometric transformations of translation and rotation were used to build the virtual rooms, using HTML page hierarchies structures, and inserting each polyhedron in its respective virtual room. The resources presented in this work can be used in the classroom to visualize polyhedra with immersive

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Voytekhovsky, Yury L. "Ordering of convex polyhedra and the Fedorov algorithm." Acta Crystallographica Section A Foundations and Advances 73, no. 1 (2017): 77–80. http://dx.doi.org/10.1107/s2053273316017095.

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A method of naming any convex polyhedron by a numerical code arising from the adjacency matrix of its edge graph has been previously suggested. A polyhedron can be built using its name. Classes of convexn-acra (i.e.n-vertex polyhedra) are strictly (without overlapping) ordered by their names. In this paper the relationship between the Fedorov algorithm to generate the whole combinatorial variety of convex polyhedra and the above ordering is described. The convexn-acra are weakly ordered by the maximum extra valencies of their vertices. Thus, non-simplen-acra follow the simple ones for anyn.

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Chang, Yi-Jun, and Hsu-Chun Yen. "Improved Algorithms for Grid-Unfolding Orthogonal Polyhedra." International Journal of Computational Geometry & Applications 27, no. 01n02 (2017): 33–56. http://dx.doi.org/10.1142/s0218195917600032.

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An unfolding of a polyhedron is a single connected planar piece without overlap resulting from cutting and flattening the surface of the polyhedron. Even for orthogonal polyhedra, it is known that edge-unfolding, i.e., cuts are performed only along the edges of a polyhedron, is not sufficient to guarantee a successful unfolding in general. However, if additional cuts parallel to polyhedron edges are allowed, it has been shown that every orthogonal polyhedron of genus zero admits a grid-unfolding with quadratic refinement. Using a new unfolding technique developed in this paper, we improve upon

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Schulte, Egon. "Polyhedra, complexes, nets and symmetry." Acta Crystallographica Section A Foundations and Advances 70, no. 3 (2014): 203–16. http://dx.doi.org/10.1107/s2053273314000217.

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Skeletal polyhedra and polygonal complexes in ordinary Euclidean 3-space are finite or infinite 3-periodic structures with interesting geometric, combinatorial and algebraic properties. They can be viewed as finite or infinite 3-periodic graphs (nets) equipped with additional structure imposed by the faces, allowed to be skew, zigzag or helical. A polyhedron or complex isregularif its geometric symmetry group is transitive on the flags (incident vertex–edge–face triples). There are 48 regular polyhedra (18 finite polyhedra and 30 infinite apeirohedra), as well as 25 regular polygonal complexes

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Kamenin, I. G., R. M. Kadushnikov, V. M. Alievsky, D. M. Alievsky, and S. V. Somina. "3-Dimensional Structure-Imitation Model of Evolution of Microstructure of Powder Body During Sintering." Textures and Microstructures 32, no. 1-4 (1999): 221–33. http://dx.doi.org/10.1155/tsm.32.221.

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This paper describes a 3D structure-imitation computer model of evolution of the powder compact during sinteringand recrystallization without nucleation. At the initial stages of the evolution processes (sintering until a mosaic structure of boundaries is formed) the model particles are spheres, and two-particle interaction laws control their evolution. During sintering the degree of mutual penetration of the particles increases, regions where spherical particles are wholly facetted by contacts with neighboring particles are formed and grow. These particles are described using the formalism of

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Subramani, K. "On the Complexities of Selected Satisfiability and Equivalence Queries over Boolean Formulas and Inclusion Queries over Hulls." Journal of Applied Mathematics and Decision Sciences 2009 (July 20, 2009): 1–18. http://dx.doi.org/10.1155/2009/845804.

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This paper is concerned with the computational complexities of three types of queries, namely, satisfiability, equivalence, and hull inclusion. The first two queries are analyzed over the domain of CNF formulas, while hull inclusion queries are analyzed over continuous and discrete sets defined by rational polyhedra. Although CNF formulas can be represented by polyhedra over discrete sets, we analyze them separately on account of their distinct structure. In particular, we consider the NAESAT and XSAT versions of satisfiability over HornCNF, 2CNF, and Horn⊕2CNF formulas. These restricted famil

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Romanova, Viktoryna A. "Visualizing surface formation of semi-regular polyhedra of Archimedes." Structural Mechanics of Engineering Constructions and Buildings 16, no. 4 (2020): 279–89. http://dx.doi.org/10.22363/1815-5235-2020-16-4-279-289.

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The most common method of forming semi-control polyhedra consists in cutting off angles and ribs of regular polyhedra by planes. The aim of the work - to consider the automated formation of a number of surfaces of semi-regular Archimedean polyhedra based on the dodecahedron. These include the truncated dodecahedron, the icosododecahedron, the romboicosododecahedron and the truncated icosododecahedron. The formation of surfaces is carried out by the kinematic method in AutoCAD using programs compiled in the AutoLISP language. Methods. The methodology for the formation of these polyhedra provide

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Barequet, Gill. "DCEL." International Journal of Computational Geometry & Applications 08, no. 05n06 (1998): 619–36. http://dx.doi.org/10.1142/s0218195998000308.

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In this paper we describe the DCEL system: a geometric software package which implements a polyhedral programming environment. This package enables fast prototyping of geometric algorithms for polyhedra or for polyhedral surfaces. We provide an overview of the system's functionality and demonstrate its use in several applications.

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Zhang, Tingting, Yuchao Gu, Xiaohan Liu, et al. "Incidence of Carassius auratus Gibelio Gill Hemorrhagic Disease Caused by CyHV-2 Infection Can Be Reduced by Vaccination with Polyhedra Incorporating Antigens." Vaccines 9, no. 4 (2021): 397. http://dx.doi.org/10.3390/vaccines9040397.

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Encapsulation of antigens within protein microcrystals (polyhedra) is a promising approach for the stable delivery of vaccines. In this study, a vaccine was encapsulated into polyhedra against cyprinid herpesvirus II (CyHV-2). CyHV-2 typically infects gibel carp, Carassius auratus gibelio, causing gill hemorrhagic disease. The vaccine was constructed using a codon-optimized sequence, D4ORF, comprising the ORF72 (region 1–186 nt), ORF66 (region 993–1197 nt), ORF81 (region 603–783 nt), and ORF82 (region 85–186 nt) genes of CyHV-2. The H1-D4ORF and D4ORF-VP3 sequences were, respectively, obtained

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DORWARD, SUSAN E. "A SURVEY OF OBJECT-SPACE HIDDEN SURFACE REMOVAL." International Journal of Computational Geometry & Applications 04, no. 03 (1994): 325–62. http://dx.doi.org/10.1142/s0218195994000185.

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We present a survey of the hidden surface removal literature, focusing on object-space algorithms. We give a brief definition and history of the problem, followed by a discussion of problems and algorithms associated with the priority ordering of faces. We go on to examine object-space algorithms in order of increasing object complexity: xy-parallel rectangles, ordered triangles, c-oriented faces, c-oriented polyhedra, polyhedral terrains, and general polyhedra. We also review recent work on merging visibility maps and moving viewpoints. Finally, we present a list of open problems.

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Laval, Jean-Paul. "The low-temperature barium fluoridozirconate variety α-BaZr2F10". Acta Crystallographica Section C Structural Chemistry 75, № 11 (2019): 1482–87. http://dx.doi.org/10.1107/s205322961901297x.

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The low-temperature triclinic variety α-BaZr2F10 constitutes a new structure type, less symmetrical than the higher-temperature β-variety. It is based on the stacking of double sheets of Zr polyhedra, connecting three different kinds of ZrF7 polyhedra and one ZrF8 polyhedron via vertices and edges, separated by corrugated Ba2+ layers. It is compared to the high-temperature β-variety, directly recrystallizing from barium fluoridozirconate glass, and also to BaTe2F10 and KTe2F9.

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Obikhod, Tetiana. "FORMATION OF MODERN MATHEMATICAL APPROACH TO SOLVING PROBLEMS OF PHYSICS." Physical and Mathematical Education 33, no. 1 (2022): 26–29. http://dx.doi.org/10.31110/2413-1571-2022-033-1-004.

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Formulation of the problem. Precision studies of the Higgs boson, supersymmetric particles, the magnetic moment of the muon, electric dipole moment of the electron, flavor anomalies demonstrate the deviation beyond Standard Model. They are connected with a new understanding of quantum field theory through the unification of gravity with particle physics in the framework of string theory - the powerful instrument, which has changed the theory picture. The article is devoted to the study of new physics through these two components. First, we considered particle physics in terms of the latest exp

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Voytekhovsky, Yury L. "How to name and order convex polyhedra." Acta Crystallographica Section A Foundations and Advances 72, no. 5 (2016): 582–85. http://dx.doi.org/10.1107/s2053273316010846.

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In this paper a method is suggested for naming any convex polyhedron by a numerical code arising from the adjacency matrix of its edge graph. A polyhedron is uniquely fixed by its name and can be built using it. Classes of convexn-acra (i.e.n-vertex polyhedra) are strictly ordered by their names.

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Domoto, Yuya, Kidai Yamamoto, Shumpei Horie, Zhengsu Yu, and Makoto Fujita. "Amplification of weak chiral inductions for excellent control over the helical orientation of discrete topologically chiral (M₃L₂)_n polyhedra." Chemical Science 13, no. 15 (2022): 4372–76. http://dx.doi.org/10.1039/d2sc00111j.

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Superb control over the helical chirality of highly-entangled (M3L2)n polyhedra (M = Cu(i), Ag(i); n = 2,4,8) was achieved via multiplication of weak chiral inductions by side chains accumulated on the huge polyhedral surfaces.

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Bobik, Thomas A., Gregory D. Havemann, Robert J. Busch, Donna S. Williams, and Henry C. Aldrich. "The Propanediol Utilization (pdu) Operon ofSalmonella enterica Serovar Typhimurium LT2 Includes Genes Necessary for Formation of Polyhedral Organelles Involved in Coenzyme B12-Dependent 1,2-Propanediol Degradation." Journal of Bacteriology 181, no. 19 (1999): 5967–75. http://dx.doi.org/10.1128/jb.181.19.5967-5975.1999.

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ABSTRACT The propanediol utilization (pdu) operon ofSalmonella enterica serovar Typhimurium LT2 contains genes needed for the coenzyme B12-dependent catabolism of 1,2-propanediol. Here the completed DNA sequence of the pduoperon is presented. Analyses of previously unpublished pduDNA sequence substantiated previous studies indicating that thepdu operon was acquired by horizontal gene transfer and allowed the identification of 16 hypothetical genes. This brings the total number of genes in the pdu operon to 21 and the total number of genes at the pdu locus to 23. Of these, six encode proteins o

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Wang, Lihua, Tamer Z. Salem, Dean J. Campbell, Colin M. Turney, C. M. Senthil Kumar, and Xiao-Wen Cheng. "Characterization of a virion occlusion-defective Autographa californica multiple nucleopolyhedrovirus mutant lacking the p26, p10 and p74 genes." Journal of General Virology 90, no. 7 (2009): 1641–48. http://dx.doi.org/10.1099/vir.0.010397-0.

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Nucleopolyhedroviruses (NPVs), family Baculoviridae, are insect-specific viruses with the potential to control insect pests in agriculture and forestry. NPVs are occluded in polyhedral occlusion bodies. Polyhedra protect virions from inactivation in the environment as well as assisting virions in horizontal transmission in the insect population. The process of virion occlusion in the polyhedra is undefined and the genes that regulate the virion occlusion process have not been well investigated yet. An Autographa californica multiple nucleopolyhedrovirus (AcMNPV) mutant (AcDef) that has a 2136

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Kovács, Flórián. "Twofold orthogonal weavings on cuboids." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2187 (2016): 20150576. http://dx.doi.org/10.1098/rspa.2015.0576.

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Some closed polyhedral surfaces can be completely covered by two-way, twofold (rectangular) weaving of strands of constant width. In this paper, a construction for producing all possible geometries for such weavable cuboids is proposed: a theorem on spherical octahedra is proven first that all further theory is based on. The construction method of weavable cuboids itself relies on successive truncations of an initial tetrahedron and is also extended for cases of degenerate (unbounded) polyhedra. Arguments are mainly based on the plane geometry of the development of the respective polyhedra, in

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Floater, Michael S. "Generalized barycentric coordinates and applications." Acta Numerica 24 (April 27, 2015): 161–214. http://dx.doi.org/10.1017/s0962492914000129.

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This paper surveys the construction, properties, and applications of generalized barycentric coordinates on polygons and polyhedra. Applications include: surface mesh parametrization in geometric modelling; image, curve, and surface deformation in computer graphics; and polygonal and polyhedral finite element methods.

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Izmestiev, Ivan. "Infinitesimal Rigidity of Convex Polyhedra through the Second Derivative of the Hilbert–Einstein Functional." Canadian Journal of Mathematics 66, no. 4 (2014): 783–825. http://dx.doi.org/10.4153/cjm-2013-031-9.

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Abstract. The paper presents a new proof of the infinitesimal rigidity of convex polyhedra. The proof is based on studying derivatives of the discrete Hilbert–Einstein functional on the space of “warped polyhedra” with a fixed metric on the boundary.The situation is in a sense dual to using derivatives of the volume in order to prove the Gauss infinitesimal rigidity of convex polyhedra. This latter kind of rigidity is related to the Minkowski theorem on the existence and uniqueness of a polyhedron with prescribed face normals and face areas.In the spherical space and in the hyperbolic-de Sitte

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Lengyel, András. "Volume-Increasing Inextensional Deformations of Platonic Polyhedra." Mathematics 13, no. 4 (2025): 645. https://doi.org/10.3390/math13040645.

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It is known that the volume of a convex polyhedron can be increased by suitable isometric deformation of its surface resulting in a non-convex shape. Deformation patterns and the associated enclosed volumes of the Platonic polyhedra were theoretically and numerically investigated by a few authors in the past. In this paper, a generic diamond-shaped folding pattern for all Platonic polyhedra is presented, optimised to achieve the maximum enclosed volumes. The numerically obtained volume increases (44.70%, 25.12%, 13.86%, 10.61%, and 4.36% for the regular tetrahedron, cube, octahedron, dodecahed

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Stojanovic, Milica. "Minimal 3-triangulations of p-toroids." Filomat 37, no. 1 (2023): 115–25. http://dx.doi.org/10.2298/fil2301115s.

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It is known that we can always 3-triangulate (i.e. divide into tetrahedra with the original vertices) convex polyhedra but not always non-convex ones. Polyhedra topologically equivalent to ball with p handles, shortly p-toroids, cannot be convex. So, it is interesting to investigate possibilities and properties of their 3-triangulations. Here we study the minimal number of necessary tetrahedra for the triangulation of a 3-triangulable p-toroid. For that purpose, we developed the concept of piecewise convex polyhedron and that of its connection graph.

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