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Relevant bibliographies by topics / Polyhedra in art

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Academic literature on the topic 'Polyhedra in art'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 February 2023

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Journal articles on the topic "Polyhedra in art"

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KRIVOSHAPKO, S. N. "POLYHEDRA AND QUASI- POLYHEDRA IN ARCHITECTURE OF CIVIL AND INDUSTRIAL ERECTIONS." Building and reconstruction 90, no. 4 (2020): 48–64. http://dx.doi.org/10.33979/2073-7416-2020-90-4-48-64.

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Innovative spatial forms appear and develop at the joint of science, art, and architecture. Geometry is the most important, fundamental components of architectural forming. Now, having passed the stages of passion for the large-span shells, the sky-scrapers, typical inexpensive buildings, architectural bionics and ergonomics; pneumatic, membrane, wire rope and shrouds erections, the architects and designers payed attention at analytically non-given forms of erections and at the polyhedron. It is noticeably especially at the last 10-15 years. In a paper, the problems of application of the polyhedron and their modifications in architecture, building, and technics are analyzed. They consider prisms, pyramids, prismatoids, Platonic and several Archimedean solids, quasi-polyhedrons, and some figures constituted on their base. Polyhedral domes, umbrella shells, and hipped plate constructions are presented too. Large quantity of the illustrations devoted to the architecture of buildings and erections, to the landscape architecture and to the sculptural compositions is presented for the confirmation of increasing interest to these structures. 31 titles of the used original sources are given.

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Luminet, Jean-Pierre. "Science, art and geometrical imagination." Proceedings of the International Astronomical Union 5, S260 (January 2009): 248–73. http://dx.doi.org/10.1017/s1743921311002377.

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AbstractFrom the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental rôle of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Dürer, Kepler, Escher, Grisey or the author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as symmetry, regular polyhedra, laws of harmonic proportion, tessellations, group theory, etc., as well as on beauty, conciseness and an emotional approach of the world.

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Polimeni, Beniamino. "PRODUCING DESIGN OBJECTS FROM REGULAR POLYHEDRA: A PRACTICAL APPROACH." Boletim da Aproged, no. 34 (December 2018): 49–55. http://dx.doi.org/10.24840/2184-4933_2018-0034_0007.

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In the last few years, digital modelling techniques have played a major role in architecture and design, influencing, at the same time, the creative process and the fabrication of objects. This revolution has produced a new productive generation of architects and designers focused on the expanding possibilities of material and formal production, reinforcing the idea of architecture as an interaction between art and artisanship. This original perspective inspires this paper, which illustrates the contemporary scenario and provides some practical guidance about tools and technologies the designers most often use for creating geometric sculptures with 3D printing. Creative possibilities of topological mesh modelling are used to generate complex geometries from regular polyhedra. This process explores how combining different geometric operations can activate architectural inquiry and generate fascinating shapes with creative flexibility.

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Coolsaet, Kris, and Stan Schein. "Some New Symmetric Equilateral Embeddings of Platonic and Archimedean Polyhedra." Symmetry 10, no. 9 (September 5, 2018): 382. http://dx.doi.org/10.3390/sym10090382.

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The icosahedron and the dodecahedron have the same graph structures as their algebraic conjugates, the great dodecahedron and the great stellated dodecahedron. All four polyhedra are equilateral and have planar faces—thus “EP”—and display icosahedral symmetry. However, the latter two (star polyhedra) are non-convex and “pathological” because of intersecting faces. Approaching the problem analytically, we sought alternate EP-embeddings for Platonic and Archimedean solids. We prove that the number of equations—E edge length equations (enforcing equilaterality) and 2 E − 3 F face (torsion) equations (enforcing planarity)—and of variables ( 3 V − 6 ) are equal. Therefore, solutions of the equations up to equivalence generally leave no degrees of freedom. As a result, in general there is a finite (but very large) number of solutions. Unfortunately, even with state-of-the-art computer algebra, the resulting systems of equations are generally too complicated to completely solve within reasonable time. We therefore added an additional constraint, symmetry, specifically requiring solutions to display (at least) tetrahedral symmetry. We found 77 non-classical embeddings, seven without intersecting faces—two, four and one, respectively, for the (graphs of the) dodecahedron, the icosidodecahedron and the rhombicosidodecahedron.

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Sarhangi, Reza. "An Art and Technology Approach to Actively Engage Students in the Mathematics of the Regular Polyhedra." Mathematics Education Trends and Research 2014 (2014): 1–10. http://dx.doi.org/10.5899/2014/metr-00060.

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Verheyen, Hugo F. "Concepts Of The Golden Diamond." International Journal of Space Structures 11, no. 1-2 (April 1996): 193–209. http://dx.doi.org/10.1177/026635119601-225.

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The regular diamond whose diagonals are in the golden proportion is commonly known as rhombus aureus or the golden diamond.a Situated in the geometric realm of polytopes, this diamond is the constituent face of a thirty-faceted zonohedron (a polyhedron composed of diamond faces), namely the rhombic triacontahedron, which has a dual relationship with an Archimedean solid and is illustrated in this article. To complete theoretical preliminaries, the triacontahedron is here derived in a new way by a particular group-theoretical approach in order to provide a generalized understanding of regularity with polyhedra. Following this, the golden diamond is observed from an artistic angle since it seems to appear particularly attractive. An explanation of this special aspect is suggested. Further, the golden diamond reveals remarkable geometrical properties, some of which are not so commonly known. These are given closer consideration. And at last, from a constructive point of view, the golden diamond proves to be well applicable to all kinds of design, going from architecture to interior design. The morphological and main part of this article supplies information on some constructive capacities of the golden diamond, in addition to unpublished applications. Two major kinds of examples concerning exterior and interior Architecture are thus presented and richly illustrated. These are: the Great Pyramid on a macro-scale, and personnally constructed art objects (with light within) on a micro-scale.

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Gould, R. O. "An adventure in multi-dimensional space: the art and geometry of polygons, polyhedra and polytypesby J. Miyazaki." Acta Crystallographica Section A Foundations of Crystallography 43, no. 6 (November 1, 1987): 840. http://dx.doi.org/10.1107/s0108767387098398.

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Emmerich, David Georges. "From Gravitation Toward Levitation." International Journal of Space Structures 11, no. 1-2 (April 1996): 3–12. http://dx.doi.org/10.1177/026635119601-202.

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Architecture is the art of defining and realising forms. Its morphological language was developed progressively, laying the foundation for a specific space-vocabularly. After being an inhabitant of caverns, the homo faber started to recreate the same kind of cavities, using the same ponderous stone material. During this process, a small set of forms was discovered: cone, pyramid, cylinder, prism and sphere. The comprise, alone or in juxtaposition, dissected or interpenetrated, our architecture to date. Today, the production of high strength materials, efficient especially in tension allows a further step toward more differentiated structural compositions, both in the matter of their components and their overall shapes. The basic morphology of these extremely light structural configurations contains a whole range of forms: antiprisms, polyhedra, torus, space-packings, all kind of hyper-spatial arrangements, creating a completely new architectural vocabulary.

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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 (July 1, 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 bp DNA deletion, including p26, p10 and p74 genes, has been isolated. No virions were detected in the polyhedra of AcDef. Restoration of all the missing sequences into AcDef led to proper virion occlusion. Individual gene deletion of either p10 or p26 could not abolish virion occlusion in the polyhedra of AcMNPV, but p10 deletion reduced virion occlusion efficiency more than threefold compared with the wild-type AcMNPV. Previous studies by other research groups on deletion of AcMNPV gene p74 suggested that p74 is a per os infectivity factor, and deletion of the p74 gene did not eliminate virion occlusion. Collectively, the three genes (p26, p10 and p74) may act in concert to regulate the virion occlusion process. Therefore, p26, p10 and p74 are all required for proper virion occlusion in the polyhedra of AcMNPV.

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Rios, Paulo Rangel, Martin E. Glicksman, and Daniel Lewis. "Advances in Grain Growth Theory." Materials Science Forum 715-716 (April 2012): 211–18. http://dx.doi.org/10.4028/www.scientific.net/msf.715-716.211.

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The theoretical description of grain growth was based for many years on the so-calledspherical model. The spherical model represents a polyhedral grain with N faces and a volume, V ,by a sphere with an equal volume having the equivalent grain radius, R. That model leads to severalinteresting results concerning normal and abnormal grain growth as well as grain size distribution.Nevertheless, representation of grains by spheres entails a fundamental limitation: namely, all topo-logical information of the polyhedral grain is forsaken. The rich variety of grain shapes occurringin three-dimensional polycrystalline networks, however, makes their energetic and kinetic analysesextremely difficult. To simplify analyses of isotropic polycrystals, average N-hedra and generalizedN-hedra ANHs or GNHs .N D 3; 4; 5;1/ were created as a set of regular polyhedra, consisting ofN identical faces that act as topological proxies for analyzing irregular grains containing N mixedfaces. The adoption of ANH/GNH as representations of polyhedral grains led to further progress inour understanding of grain growth, particularly those aspects related to topological behavior. This pa-per summarizes some recent advances of representing polyhedral grains by ANHs/GNHs rather thanby spheres.

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Dissertations / Theses on the topic "Polyhedra in art"

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Letchford, Adam Nicholas. "Polyhedral results for some constrained arc-routing problems." Thesis, Lancaster University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.337546.

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Andrews, Noam. "Irregular Bodies: Polyhedral Geometry and Material Culture in Early Modern Germany." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493270.

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The dissertation explores the centrality of the Platonic Solids, and polyhedral geometry generally, to the artistic and mixed-mathematical cultures of Renaissance Germany. Beginning with Albrecht Dürer’s groundbreaking treatise on geometry, the Underweyung der Messung (1525), the dissertation redefines sites of early modern experimentation to include the graphical spaces in which new geometrical knowledge was practiced, invented, contested, manipulated, discarded, and presented. The research describes the historical contexts and development of the practice of polyhedral geometry over the course of the 16th century, expanding from Dürer to the lesser-known textbooks for practical geometry that his work inspired in Germany, and continuing with epitomes of the polyhedral genre, namely Wenzel Jamnitzer’s Perspectiva corporum regularium (1568) and the drawings of the Augsburg artisan Lorentz Stöer. The dissertation then follows the migration of polyhedra into intarsia and turned-ivory artifacts used for teaching applied geometry to European aristocracy, and concludes by addressing the polyhedral cosmology of the astronomer Johannes Kepler. By tracing the lifespan of polyhedra from their use as perspectival tools and pedagogical devices in Renaissance workshops into courtly Kunstkammern and onto the precious surfaces of domestic objects, the dissertation uncovers the influence that the decorative arts had on the conceptualization of geometrical knowledge and its new engagement with materials and concepts of materiality.
History of Science

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Clarke, David John, and d. clarke@irl cri nz. "The Synthesis and Characterisation of Polyhedral Oligomeric Silsesquioxane Bound Chromophores." Flinders University. School of Chemistry, Physics and Earth Sciences, 2008. http://catalogue.flinders.edu.au./local/adt/public/adt-SFU20080908.074728.

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This research involved the synthesis and characterisation of a range of optically active polyhedral oligomeric silsesquioxane (POSS) compounds. POSS precursor compounds containing functional groups required for subsequent attachment of the desired functional groups have been synthesised. Examples of such precursor compounds include mono-functionalised POSS compounds with periphery aldehyde, azide, amino and pyridyl functional groups. A variety of POSS compounds, functionalised with a range of optical functionalities, including optical limiters such as fulleropyrrolidine and iminofullerene, and dyes and pigments, including naphthalene, biphenyl, perylene, pyrene and porphyrin have been synthesised. The reaction of mono-functionalised POSS aldehydes with fullerene (C60) in the presence of N-methylglycine yielded the desired POSS fulleropyrrolidines, whilst reaction of mono-functionalised POSS azide with C60 yielded POSS iminofullerenes. All POSS fullerene compounds were characterised by power limiting measurements, exhibiting comparable power limiting to that of parent C60. The microwave condensation of mono-amino POSS with a range of mono- and bis-anhydrides yielded the POSS imide compounds, which were characterised by UV-Vis and fluorescence spectrophotometry. The perylene POSS imide derivative was further characterised by single crystal x-ray crystallography. The naphtha and biphenyl POSS imides exhibited extremely weak fluorescence, whilst the perylene ii POSS imide displayed particularly strong fluorescence, with a quantum yield approaching unity. The incorporation of a pyridyl group on the periphery of a mono-functionalised POSS cage allowed for the synthesis of the first porphyrin functionalised POSS compound. Mono-porphyrin POSS exhibited comparable absorption properties to other pyridyl ligated ruthenium porphyrins. Mono-functionalised pyrene POSS compounds were prepared through the reaction of 1-pyrene acid chloride with mono(3-aminopropyl)POSS. This synthetic pathway offered a convenient route to mono-functionalised pyrene POSS, in preference to the multi-substitution associated with Heck coupling. Mono-pyrene POSS was determined to be strongly fluorescent, exhibiting a high quantum yield of fluorescence

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Farmer, Catherine Elizabeth. "Surface Characterization of Siloxane, Silsesquioxane, and Maleic Anhydride Containing Polymers at Air/Liquid Interfaces." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/32408.

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Langmuir-monolayer formation at the air/water interface (A/W) can be achieved by spreading amphiphilic molecules on a liquid subphase and compressing them into an ordered arrangement. The use of the Langmuir-Blodgett technique (LB) to prepare ultra thin films on solid surfaces from monolayers at A/W has considerable utility for studying surface interactions. In particular, the phase behavior of polyhedral oligomeric silsesquioxanes (POSS) was examined using a combination of LB and Brewster angle microscopy (BAM).Polymer fillers have been shown to reduce the cost and often improve the properties of high performance polymer composites. The utility of POSS as a potential nanofiller in blends with polymers such as poly(dimethylsiloxane) (PDMS) and poly(vinylacetate) (PVAc) was explored using surface pressure-area per monomer isotherms (P-A) and BAM. Substantial morphological differences are seen between polymer blends with heptasubstituted trisilanol-POSS and fully condensed octasubstituted-POSS due to differences in subphase affinity.Several poly(1-alkene-alt-maleic anhydride) (PXcMA) polymers were studied at both the gas/liquid interface as Langmuir films and at the gas/solid interface as Langmuir-Blodgett thin films on silicon substrates. A 0.01 M HCl solution (pH~2) was used during film deposition to ensure the carboxylic acids were fully protonated. The PXcMA polymers included X=1-hexene, 1-octene, 1-decene, and 1-octadecene (represented as PHcMA, POcMA, PDcMA, and PODcMA respectively). The P-A isotherms of these polymers were consistent with those obtained previously.1Tensiometry was used to determine the critical micelle concentrations (c.m.c.) of variable molar mass poly(dimethylsiloxane-b-(3-cyanopropyl)methylsiloxane-b-dimethylsiloxane) (PDMS-PCPMS-PDMS) triblock copolymers and a poly(dimethylsiloxane-b-2-ethyl-2-oxazoline) diblock copolymer. Dynamic light scattering (DLS) corroborated interfacial tension results. The polymers exhibited well-defined temperature-independent c.m.c.'s. These measurements ensured that the synthesis of cobalt nanoparticles for biocompatible magnetic fluids occurred above the c.m.c.
Master of Science

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Slaight-Brown, Shannon M. "Restoration." VCU Scholars Compass, 2017. http://scholarscompass.vcu.edu/etd/4890.

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The marks I make in clay have different characteristics, and the physical mark of one’s fingertips or visual record of the hand is personal and intimate. This visible activity is the evidence of my constant presence and control within each object. Its repetitive meditation produces a private relief from my persistent anxieties. This exploration for me is not only visual, but also physical. This is the start of my infatuation with the idea of pattern. It has its own discrete visual language and modes of communication; and through my research I am developing a method of intercommunication.

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Books on the topic "Polyhedra in art"

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Origami polyhedra design. Wellesley, Mass: A K Peters, 2009.

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A Constellation of Origami Polyhedra. Mineola, New York: Dover Publications, 2004.

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A Plethora of Polyhedra in Origami. New York: Dover Publications, 2002.

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Platons former i skrift, konst, teknik och naturvetenskap. Stockholm: Carlssons, 2008.

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An adventure in multidimensional space: The art and geometry of polygons, polyhedra, and polytopes. New York: Wiley, 1986.

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Unit Polyhedron Origami. Tokyo, Japan: Japan Publications, 2006.

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Geometrix: 161 patterns and motifs for artists and designers. New York: Dover Publications, 1991.

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1990-, Mann Elissa, ed. Cool flexagon art: Creative activities that make math & science fun for kids! Minneapolis, Minnesota: ABDO Publishing Company, 2014.

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Josep, Casamartina i. Parassols, Fondevila Mariàngels, and Fundació Palau, eds. Palau Oller polièdric: Palau Oller poliédrico = Palau Oller polyhedric. Caldes d'Estrac [Spain]: Fundació Palau, 2010.

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Montroll, John. Origami Polyhedra Design. CRC Press LLC, 2009.

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Book chapters on the topic "Polyhedra in art"

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Angell, Ian O., and Cathy Sobhanpanah. "Oct-Tree Encoding and Fractal Rendering of Polyhedra." In Computers in Art, Design and Animation, 140–50. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-4538-4_10.

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Messina, Barbara, and Stefano Chiarenza. "Drawing and Geometric Constructions of Polyhedra in the Art of Escher." In Advances in Intelligent Systems and Computing, 895–903. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-63403-2_81.

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Grünbaum, Branko. "Are Your Polyhedra the Same as My Polyhedra?" In Algorithms and Combinatorics, 461–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55566-4_21.

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Roelofs, Rinus. "Double Layered Polyhedra." In Handbook of the Mathematics of the Arts and Sciences, 879–959. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-319-57072-3_23.

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Roelofs, Rinus. "Double Layered Polyhedra." In Handbook of the Mathematics of the Arts and Sciences, 1–82. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-319-70658-0_23-1.

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Eglese, Richard W., and Adam N. Letchford. "Polyhedral Theory for Arc Routing Problems." In Arc Routing, 199–230. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-4495-1_6.

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Glaeser, Georg. "Polyhedra: multi-faced and multi-sided." In Geometry and its Applications in Arts, Nature and Technology, 87–124. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61398-3_3.

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Streinu, Ileana. "Paneled and Molecular Polyhedra: How Stable Are They?" In Shaping Space, 201–9. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-0-387-92714-5_14.

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Kleinschmidt, Peter, and Shmuel Onn. "Oriented matroid polytopes and polyhedral fans are signable." In Integer Programming and Combinatorial Optimization, 198–211. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-59408-6_52.

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Velezmoro-León, Ricardo, Robert Ipanaqué-Chero, Marcela Velásquez Fernández, and Jorge Jimenez Gomez. "Construction of Polyhedra Whose Vertices are Points on Curve Which Lying on Lemniscatic Torus with Mathematica." In Computational Science and Its Applications – ICCSA 2021, 3–17. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-86960-1_1.

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Conference papers on the topic "Polyhedra in art"

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Maza, Stéphane, Jean-Claude Léon, and Frédéric Noël. "Mesh Construction Dedicated to a Multi-Representation for Structure Analysis Based on an Initial Polyhedral Geometry." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/cie-4446.

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Abstract The aim of this paper is to present the first part of a new approach devoted to the generation of a data structure and operators for the hierarchical representation of 3D polyhedra. Here are described the treatments which allow to create some of the elements of this hierarchical model. At first, partitions of the initial polyhedron are mapped into planar connex hulls. Then, these domains are used like a piecewise parametric 2D space for subsequent polyhedra generations. In order to create such a mapping, the initial 3D polyhedron is partitioned to produce simply convex subsets which can be submitted to the parametrization process. The next step consists in the generation of a minimum representation of the initial 3D polyhedron. This representation forms the root of the hierarchical data structure. Then, the mapping obtained allows the construction of various polyhedral representations of the initial geometry. Criteria related to 3D parameters are used to generate the range of polyhedra. The reverse mapping (from 2D to 3D) helps reduce the computing cost required to generate 3D polyhedra. Each 3D polyhedron generation is carried out under 3D geometric criteria depending on the context. i.e.: structural analysis, levels of details of a geometric model, ... Among the goals of the hierarchical data structure, the unification and the inter dependency of the meshes required to carry out the structural analysis of a part occupies a central position.

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Ota, Matheus J., Flávio K. Miyazawa, and Phablo F. S. Moura. "The Balanced Connected k-Partition Problem: Polyhedra and Algorithms." In Concurso de Teses e Dissertações da SBC. Sociedade Brasileira de Computação, 2021. http://dx.doi.org/10.5753/ctd.2021.15763.

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The balanced connected k-partition (BCPk) problem consists in partitioning a connected graph into connected subgraphs with similar weights. This problem arises in multiple practical applications, such as police patrolling, image processing, data base and operating systems. In this work, we address the BCPk using mathematical programming. We propose a compact formulation based on flows and a formulation based on separators. We introduce classes of valid inequalities and design polynomial-time separation routines. Moreover, to the best of our knowledge, we present the first polyhedral study for BCPk in the literature. Finally, we report on computational experiments showing that the proposed algorithms significantly outperform the state of the art for BCPk.

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Liu, C. Y., and R. W. Mayne. "Distance Calculations in Motion Planning Problems With Interference Situations." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0018.

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Abstract This paper discusses distance calculations for three dimensional polyhedra with the assumption of convex bodies. An n-surface convex polyhedron is viewed as the intersection of n half-spaces and is represented by n linear inequality equations while the square of the distance between two points is of a quadratic form in terms of two sets of x-y-z coordinates. The static distance-to-contact between two non-interfering convex polyhedral shapes is then directly solvable by quadratic programming. Based on the concept of distance-past-contact, distance calculations for situations with interference are presented and tested in optimization based robot path planning examples. The distance evaluation is further investigated for the dynamic situations by a swept volume computation strategy. The approach is illustrated in examples with a moving robot link and a fixed obstacle.

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Stine, William Wren, and Montie McMickell. "Stereopsis and the discrimination of rigidity." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.thvv1.

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Isometric projections of three-dimensional, rigidly rotating polyhedra appear to deform under certain circumstances (Green, 1961, JEP). Relative to those that appear to be rigid, rigidly rotating polyhedra that appear to deform are more difficult to discriminate from ones that actually deform during rotation (Sparrow and Stine, 1990, ARVO). When a rigidly rotating polyhedron appears to deform, the introduction of retinal disparity can result in the perception of rigidity (Sparrow and Stine, 1987a, ARVO). We used polyhedra that were configured either to appear nonrigid or to appear rigid while rigidly rotating (see Sparrow and Stine, 1987b, 1988, OSA). These two classes of stimuli were then presented, one at a time, rotating rigidly (noise trials) or rotating with real deformations (signal + noise trials). Sensitivity to real deformations was less for polyhedra that were more likely to appear to deform than for those that were more likely to appear rigid (replicating Sparrow and Stine, 1990). Adding disparity to a stereo pair of polyhedra that appear to deform can increase sensitivity to real deformations. However, one stereo-blind subject showed no increase in sensitivity with disparity. Disparity allows the subject to see the rigidity of the polyhedron and then discriminate deforming from non-deforming stimuli.

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Zhang, Ying, Hai-Jun Su, Qizheng Liao, Shimin Wei, and Weiqing Li. "New Synthesis Approach for Expandable Polyhedral Linkages." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-35114.

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This paper presents a new synthesis approach for expandable polyhedral linkages, which are synthesized by inserting appropriate link groups into the faces of polyhedron and interconnecting them by a special composite hinges (called gusset by K. Wohlhart). The overconstrained expandable polyhedral linkages are movable with one degree of freedom (DOF).The link groups are single DOF scaling planar linkages. The gussets are multiple rotary joints whose axes converge at the corresponding vertices of the polyhedron and the number of the rotary joints equals the one of the faces which meet at the vertices. This new approach is suitable for any polyhedron whatever is regular or irregular polyhedron. To verify this new approach, the expandable regular hexahedral linkage is modeled in the SolidWorks and its mobility are studied based on screw theory and topology graph.

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Hobbs, Linn W. "What Can Topological Models Tell Us About Glass Structure and Properties?" In Bragg Gratings, Photosensitivity, and Poling in Glass Fibers and Waveguides. Washington, D.C.: Optica Publishing Group, 1997. http://dx.doi.org/10.1364/bgppf.1997.jsua.2.

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Atomic arrangements in condensed matter partition three-dimensional space into polyhedra whose edges are interatomic vectors. These polyhedra, formally known as void polytopes, fill (tesselate) space, and their identity and arrangement can provide one description of a given atomic arrangement (Figure 1a) [1]. Other tessellations associated with space-filling of random structures are Voronoi polyhedral cells [2] and their dual the Delauney network [3]. These tessellations are relatively intuitive in two dimensions, but considerably more complex in three-dimensions—for example in tetrahedral networks like SiO2—where a set of as many as 126 void polyhedra may be required to model interstitial space [1]. Because many arrangements favor particular coordination of one atom by others, owing to bond orbital, radius ratio, or local electrostatic neutrality considerations, discrete coordination polyhedra comprise a subset of the possible void polytopes, and the structure may be described by the way in which coordination polyhedra are connected together and fill space by defining the remaining void polytopes. Space filling by connected structural units was a favorite description tool of early crystal chemists [4], and in fact the connectivity of such structural polytopes (number of polytopes sharing vertices, edges and faces) has been shown to correlate with glass-forming ability and extendability of aperiodic networks [5] and to govern the amorphizability of crystalline solids [6].

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Wilson, H. B., and G. S. Chang. "Line Integral Computation of Geometrical Properties of Plane Faces and Polyhedra." In ASME 1991 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/cie1991-0125.

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Abstract Surface integrals arising during computation of geometrical properties of volumes are studied. Line integrals are formulated which give the contributions of a general plane surface area. These integrals are evaluated to provide more concise exact formulas for the geometrical properties of polyhedra than have been obtained previously. A short computer program for polyhedron properties is presented, along with numerical examples.

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Fang, J. J., D. E. R. Clark, and J. E. L. Simmons. "Dynamic Collision Detection in Virtual Worlds Using HV Partition." In ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium collocated with the ASME 1995 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/cie1995-0818.

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Abstract In this paper, a simulated three-dimensional virtual world is created with a virtual 3D space ball for virtual object control. We propose a new technique called HV Partition to detect accurate collision on the assembly of two polyhedral solids in virtual simulation. This is a solid-based detection methodology achieved by automatically partitioning the object into smaller solid boxes. Mechanical components, represented by non-convex polyhedra, traversing any degree of freedom, are applied in tins environment. Using this HV Partition method, the accurate interference between two polyhedral objects can be found. The HV Partition methodology is applied following initial approximate collision detection using traditional bounding box and bounding sphere methods. The smaller the number of smaller boxes, the quicker is the performance of the collision algorithm. An automatic partition method is also given to reduce the number of smaller boxes in an object.

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Xi, Zhonghua, and Jyh-Ming Lien. "Polyhedra Fabrication Through Mesh Convexification: A Study of Foldability of Nearly Convex Shapes." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67212.

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A polyhedron can be unfolded to a net, i.e., an unfolding without overlapping, by carefully cutting along the surface. If the cuts are restricted only on the edges of the polyhedron, where should the cuts be? This is called an edge-unfolding problem, which has been extensively studied in the literature for centuries. Although several promising properties have been discovered, several recent preliminary works show that no valid net exists even for certain simple non-convex polyhedra. Therefore, we propose to convexify the input polyhedron before unfolding. More specifically, we remove local concave surface features via inflation simulation. We then eliminate global concave structure features by segmenting the polyhedron to a small number of part-aware and nearly convex components. Then the net for each nearly convex component can be obtained. We further show that convexified shapes can be continuously folded and can be easily realized by a physical self-folding machine Our experimental results show that the proposed convexification approaches can reduce the computation time by several folds.

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George, Derosh, Marc Madou, and Edwin A. Peraza Hernandez. "Characterization and Design of Programmable Self-Folding Polymer Films." In ASME 2020 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/smasis2020-2286.

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Abstract This paper presents the characterization and design aspects of a novel fabrication method that integrates photolithography and self-folding to create polymer polyhedral structures. A two-step UV exposure process is used to produce patterned polymer films with flexible folds of low cross-linking density and stiff faces of high cross-linking density. Solvent is diffused into the folds during the development step of the photolithography process due to their low cross-linking density. The solvent concentration is non-uniform across the thickness of the folds and causes a strain gradient at these regions when the solvent is removed by heating the films, which enables self-folding. Experiments are performed to calibrate an equation that relates the dimensions of the folds and their achieved fold angle. An analytical model is introduced to elucidate the form of the equation and provide physical meaning to the calibration parameter. The formula is incorporated into a computational implementation of the unfolding polyhedra method that considers smoothly bent folds. This method, enhanced with the experimentally calibrated formula, enables the design of planar films programmed to self-fold into target three-dimensional shapes when heated. Polyhedral shapes are fabricated to demonstrate the developed method for origami-based fabrication. A parametric study quantifying the accuracy of the designed polyhedral forms with smooth folds as compared against those with idealized creased folds is performed.

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Reports on the topic "Polyhedra in art"

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Osypova, Nataliia V., and Volodimir I. Tatochenko. Improving the learning environment for future mathematics teachers with the use application of the dynamic mathematics system GeoGebra AR. [б. в.], July 2021. http://dx.doi.org/10.31812/123456789/4628.

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Immersive technologies and, in particular, augmented reality (AR) are rapidly changing the sphere of education, especially in the field of science, technology, engineering, arts and mathematics. High- quality professional training of a future mathematics teacher who is able to meet the challenges that permeate all sides, the realities of the globalizing information society, presupposes reliance on a highly effective learning environment. The purpose of the research is to transform the traditional educational environment for training future mathematics teachers with the use of the GeoGebra AR dynamic mathematics system, the introduction of cloud technologies into the educational process. The educational potential of GeoGebra AR in the system of professional training of future mathematics teachers is analyzed in the paper. Effective and practical tools for teaching mathematics based on GeoGebra AR using interactive models and videos for mixed and distance learning of students are provided. The advantages of the GeoGebra AR dynamic mathematics system are highlighted. The use of new technologies for the creation of didactic innovative resources that improve the process of teaching and learning mathematics is presented on the example of an educational and methodological task, the purpose of which is to create didactic material on the topic “Sections of polyhedra”. While solving it, future teachers of mathematics should develop the following constituent elements: video materials; test tasks for self-control; dynamic models of sections of polyhedra; video instructions for constructing sections of polyhedra and for solving basic problems in the GeoGebra AR system. The article highlights the main characteristics of the proposed educational environment for training future mathematics teachers using the GeoGebra AR dynamic mathematics system: interdisciplinarity, polyprofessionalism, dynamism, multicomponent.

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Bilous, Vladyslav V., Volodymyr V. Proshkin, and Oksana S. Lytvyn. Development of AR-applications as a promising area of research for students. [б. в.], November 2020. http://dx.doi.org/10.31812/123456789/4409.

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The article substantiates the importance of using augmented reality in the educational process, in particular, in the study of natural and mathematical disciplines. The essence of AR (augmented reality), characteristics of AR hardware and software, directions and advantages of using AR in the educational process are outlined. It has proven that AR is a unique tool that allows educators to teach the new digital generation in a readable, comprehensible, memorable and memorable format, which is the basis for developing a strong interest in learning. Presented the results of the international study on the quality of education PISA (Programme for International Student Assessment) which stimulated the development of the problem of using AR in mathematics teaching. Within the limits of realization of research work of students of the Borys Grinchenko Kyiv University the AR-application on mathematics is developed. To create it used tools: Android Studio, SDK, ARCore, QR Generator, Math pattern. A number of markers of mathematical objects have been developed that correspond to the school mathematics course (topic: “Polyhedra and Functions, their properties and graphs”). The developed AR tools were introduced into the process of teaching students of the specialty “Mathematics”. Prospects of research in development of a technique of training of separate mathematics themes with use of AR have been defined.

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Shapovalov, Yevhenii B., Viktor B. Shapovalov, Roman A. Tarasenko, Stanislav A. Usenko, and Adrian Paschke. A semantic structuring of educational research using ontologies. [б. в.], June 2021. http://dx.doi.org/10.31812/123456789/4433.

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This article is devoted to the presentation of the semantic interoperability of research and scientific results through an ontological taxonomy. To achieve this, the principles of systematization and structuration of the scientific/research results in scientometrics databases have been analysed. We use the existing cognitive IT platform Polyhedron and extend it with an ontology-based information model as main contribution. As a proof-of-concept we have modelled two ontological graphs, “Development of a rational way for utilization of methane tank waste at LLC Vasylkivska poultry farm” and “Development a method for utilization of methane tank effluent”. Also, for a demonstration of the perspective of ontological systems for a systematization of research and scientific results, the “Hypothesis test system” ontological graph has created.

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Chejanovsky, Nor, and Bruce A. Webb. Potentiation of pest control by insect immunosuppression. United States Department of Agriculture, July 2004. http://dx.doi.org/10.32747/2004.7587236.bard.

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Our original aims were to elucidate the mechanisms through which the immunosuppressive insect virus, the Campoletis sonorensis polydnavirus (CsV) promotes replication of a well-characterized pathogenic virus, the Autographa californica multiple nucleopolyhedrovirus (AcMNPV) in hosts that are mildly or non-permissive to virus replication. According to the BARD panels criticism we modified our short-term goals (see below). Thus, in this feasibility study (one-year funding) we aimed to show that: 1. S. littoralis larvae mount an immune response against a baculovirus infection. 2. Immunosuppression of an insect pest improves the ability of a viral pathogen (a baculovirus) to infect the pest. 3. S. littoralis cells constitute an efficient tool to study some aspects of the anti- viral immune response. We achieved the above objectives by: 1. Finding melanized viral foci upon following the baculoviral infection in S . littoralis larvae infected with a polyhedra - positive AcMNPV recombinant that expressed the GFP gene under the control of the Drosophila heat shock promoter. 2. Studying the effect of AcMNPV-infection in S . littoralis immunosuppressed by parasitation with the Braconidae wasp Chelonus inanitus that bears the CiV polydna virus, that resulted in higher susceptibility of S. littoralis to AcMNPV- infection. 3. Proving that S. littoralis hemocytes resist AcMNPV -infection. 4. Defining SL2 as a granulocyte-like cell line and demonstrating that as littoralis hemocytic cell line undergoes apoptosis upon AcMNPV -infection. 5. Showing that some of the recombinant AcMNPV expressing the immuno-suppressive polydna virus CsV- vankyrin genes inhibit baculoviral-induced lysis of SL2 cells. This information paves the way to elucidate the mechanisms through which the immuno- suppressive polydna insect viruses promote replication of pathogenic baculoviruses in lepidopteran hosts that are mildly or non-permissive to virus- replication by: - Assessing the extent to which and the mechanisms whereby the immunosuppressive viruses, CiV and CsV or their genes enhance AcMNPV replication in polydnavirus- immunosuppressed H. zea and S. littoralis insects and S. littoralis cells. - Identifying CiV and CsV genes involved in the above immunosuppression (e.g. inhibiting cellular encapsulation and disrupting humoral immunity). This study will provide insight to the molecular mechanisms of viral pathogenesis and improve our understanding of insect immunity. This knowledge is of fundamental importance to controlling insect vectored diseases of humans, animals and plants and essential to developing novel means for pest control (including baculoviruses) that strategically weaken insect defenses to improve pathogen (i.e. biocontrol agent) infection and virulence.

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