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Journal articles on the topic 'Polyhedra in art'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 February 2023

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1

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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2

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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3

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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4

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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6

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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7

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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8

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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9

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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10

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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11

Lalvani, Haresh. "Non-periodic Space Structures." International Journal of Space Structures 2, no. 2 (June 1987): 93–108. http://dx.doi.org/10.1177/026635118700200204.

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An interesting class of two- and three-dimensional space structures can be derived from projections of higher-dimensional structures. Regular polygons and regular-faced polyhedra provide the geometry of families of n-stars from which two- and three-dimensional projections of n-dimensional grids can be derived. These projections are rhombic space grids composed of all-space filling rhombi and rhombohedra with edges parallel to n directions. An infinite class of single-, double- and multi-layered grids can be derived from n-sided polygons and prisms, and a finite class of multi-directional grids from the polyhedral symmetry groups. The grids can be periodic, centrally symmetric or non-periodic, and act as skeletons to generate corresponding classes of space-filling, packings and labyrinths.

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12

Rubin, Leonard R. "Topological n-cells and Hilbert cubes in inverse limits." Applied General Topology 19, no. 1 (April 2, 2018): 9. http://dx.doi.org/10.4995/agt.2018.7061.

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<p>It has been shown by S. Mardešić that if a compact metrizable space X has dim X ≥ 1 and X is the inverse limit of an inverse sequence of compact triangulated polyhedra with simplicial bonding maps, then X must contain an arc. We are going to prove that if X = (|K<sub>a</sub>|,p<sup>b</sup><sub>a</sub>,(A,)<a href="http://www.codecogs.com/eqnedit.php?latex=\preceq" target="_blank"><img title="\preceq" src="http://latex.codecogs.com/gif.latex?\preceq" alt="" /></a>)is an inverse system in set theory of triangulated polyhedra|K<sub>a</sub>|with simplicial bonding functions p<sup>b</sup><sub>a</sub> and X = lim X, then there exists a uniquely determined sub-inverse system X<sub>X</sub>= (|L<sub>a</sub>|, p<sup>b</sup><sub>a</sub>|L<sub>b</sub>|,(A,<a href="http://www.codecogs.com/eqnedit.php?latex=\preceq" target="_blank"><img title="\preceq" src="http://latex.codecogs.com/gif.latex?\preceq" alt="" /></a>)) of X where for each a, L<sub>a</sub> is a subcomplex of K<sub>a</sub>, each p<sup>b</sup><sub>a</sub>|L<sub>b</sub>|:|L<sub>b</sub>| → |L<sub>a</sub>| is surjective, and lim X<sub>X</sub> = X. We shall use this to generalize the Mardešić result by characterizing when the inverse limit of an inverse sequence of triangulated polyhedra with simplicial bonding maps must contain a topological n-cell and do the same in the case of an inverse system of finite triangulated polyhedra with simplicial bonding maps. We shall also characterize when the inverse limit of an inverse sequence of triangulated polyhedra with simplicial bonding maps must contain an embedded copy of the Hilbert cube. In each of the above settings, all the polyhedra have the weak topology or all have the metric topology(these topologies being identical when the polyhedra are finite).</p>

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13

Barbosa, Valéria C. F., João B. C. Silva, and Walter E. Medeiros. "Practical applications of uniqueness theorems in gravimetry: Part II—Pragmatic incorporation of concrete geologic information." GEOPHYSICS 67, no. 3 (May 2002): 795–800. http://dx.doi.org/10.1190/1.1484523.

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We illustrate the importance of establishing solution uniqueness through mathematical restrictions reflecting a source attribute. We also illustrate the validity and utility of a guideline derived in an accompanying paper for constructing sound gravity inversion methods for the class of sources presenting either homogeneous or depth‐independent density distributions. The two‐part guideline is (1) to introduce a priori information favoring uniqueness, either by assuming that a nonnull density distribution depending only on x and y is confined to the interior of a horizontal slab with known position or by limiting the class of possible solutions to homogeneous, simply connected polygons (or polyhedra) with known density, displaying no fancy shapes and no curling apophyses at their borders, and (2) to introduce information favoring solution stability by estimating only the features of the source which may be resolved by the data. Following the guideline, we apply different methods to gravity data using interpretation models consisting of a grid of cells on the x‐y and x‐z planes. In both cases the estimates are very close to the true synthetic source. The data produced by the distribution varying with x and z are also inverted using the method, which minimizes the norm of the first‐order derivative of the density. This constraint does not reflect a true source attribute but is strong enough to stabilize the solution and to guarantee its uniqueness. Because of the strong bias imposed to the solution, the estimated distribution, although unique and stable, is far from the true source, concentrating most of the anomalous mass at the surface. Finally, we present an alternative method which redistributes the estimated anomalous mass downward. To be effective, this technique requires prior knowledge about the source depth to the top. In addition, the source should not be too small and deep. Although being able to produce good results, this alternative method requires a great dose of the interpreter's art.

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14

Di Rocco, Sandra, Christian Haase, Benjamin Nill, and Andreas Paffenholz. "Polyhedral adjunction theory." Algebra & Number Theory 7, no. 10 (December 31, 2013): 2417–46. http://dx.doi.org/10.2140/ant.2013.7.2417.

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15

Champanerkar, Abhijit, Ilya Kofman, and Jessica S. Purcell. "Right-angled polyhedra and alternating links." Algebraic & Geometric Topology 22, no. 2 (August 3, 2022): 739–84. http://dx.doi.org/10.2140/agt.2022.22.739.

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16

Inoue, Taiyo. "Organizing volumes of right-angled hyperbolic polyhedra." Algebraic & Geometric Topology 8, no. 3 (September 15, 2008): 1523–65. http://dx.doi.org/10.2140/agt.2008.8.1523.

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17

Atkinson, Christopher K. "Volume estimates for equiangular hyperbolic Coxeter polyhedra." Algebraic & Geometric Topology 9, no. 2 (June 13, 2009): 1225–54. http://dx.doi.org/10.2140/agt.2009.9.1225.

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18

Rushton, Brian. "Constructing subdivision rules from polyhedra with identifications." Algebraic & Geometric Topology 12, no. 4 (October 27, 2012): 1961–92. http://dx.doi.org/10.2140/agt.2012.12.1961.

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19

Iriye, Kouyemon, and Daisuke Kishimoto. "Decompositions of suspensions of spaces involving polyhedral products." Algebraic & Geometric Topology 16, no. 2 (April 26, 2016): 825–41. http://dx.doi.org/10.2140/agt.2016.16.825.

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20

Flapan, Erica, Blake Mellor, and Ramin Naimi. "Complete graphs whose topological symmetry groups are polyhedral." Algebraic & Geometric Topology 11, no. 3 (May 17, 2011): 1405–33. http://dx.doi.org/10.2140/agt.2011.11.1405.

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21

Conrad, Matthias, Bernd Harbrecht, Thomas Weber, Daniel Y. Jung, and Walter Steurer. "Large, larger, largest – a family of cluster-based tantalum copper aluminides with giant unit cells. II. The cluster structure." Acta Crystallographica Section B Structural Science 65, no. 3 (May 19, 2009): 318–25. http://dx.doi.org/10.1107/s0108768109014013.

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This is the second of two papers, where we discuss the cluster structures of a novel family of cluster-based intermetallic phases of unprecedented complexity: cF444-Al63.6Ta36.4 (AT-19), a = 19.1663 (1) Å, V = 7040 Å3, cF(5928 − x)-Al56.6Cu3.9Ta39.5, x = 20 (ACT-45), a = 45.376 (1) Å, V = 93 428 Å3 and cF(23, 256 − x)-Al55.4Cu5.4Ta39.1, x = 122 (ACT-71), a = 71.490 (4) Å, V = 365 372 Å3. The space group is F\bar 43m in all three cases. The structures can be described as packings of clusters such as fullerenes, dodecahedra, pentagonal bifrusta and Friauf polyhedra. A characteristic feature of the two larger structures are nets of hexagonal bipyramidal Ta clusters (h.b.p.). The extremely short distance of 2.536–2.562 Å between their apical Ta atoms indicates unusually strong bonding. The large h.b.p. nets are sandwiched between slabs of Friauf polyhedra resembling the structure of the μ phase.

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22

Gailiunas, Paul. "Rods, helices and polyhedra." Journal of Mathematics and the Arts 15, no. 3-4 (October 2, 2021): 218–31. http://dx.doi.org/10.1080/17513472.2021.1993657.

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23

Baverel, Olivier, and Hoshyar Nooshin. "Nexorades Based on Regular Polyhedra." Nexus Network Journal 9, no. 2 (October 2007): 281–98. http://dx.doi.org/10.1007/s00004-007-0043-0.

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24

Wang, X., and F. Liebau. "Studies on bond and atomic valences. I. correlation between bond valence and bond angles in SbIII chalcogen compounds: the influence of lone-electron pairs." Acta Crystallographica Section B Structural Science 52, no. 1 (February 1, 1996): 7–15. http://dx.doi.org/10.1107/s0108768195004472.

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In the present bond-valence concept the bond-valence parameter ro is treated as constant for a given pair of atoms, and it is assumed that the bond valence sij is a function of the corresponding bond length Dij , and that the atomic valence is an integer equal to the formal oxidation number for Vi derived from stoichiometry. However, from a statistical analysis of 76 [SbIIIS n ] and 14 [SbIIISe n ] polyhedra in experimentally determined structures, it is shown that for SbIII—X bonds (X = S, Se), ro is correlated with {\bar \alpha} i , the average of the X—Sb—X angles between the three shortest Sb—X bonds. This is interpreted as a consequence of a progressive retraction of the 5s lone-electron pair from the SbIII nucleus, which can be considered as continuous change of the actual atomic valence act Vi of Sb from +3 towards +5. A procedure is derived to calculate an effective atomic valence eff Vi of SbIII from the geometry, {\bar \alpha} i and Dij , of the [SbIII Xn ] polyhedra, which approximates act Vi and is a better description of the actual valence state of SbIII than the formal valence for Vi . Calculated eff V SbIII are found to vary between +2.88 and +3.80 v.u. for [SbIIIS n ] and between +2.98 and +3.88 v.u. for [SbIIISe n ] polyhedra. It is suggested that a corresponding modification of the present bond-valence concept is also required for other cations with lone-electron pairs.

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25

Fu, Xin, and Jelena Grbić. "Simplicial G–complexes and representation stability of polyhedral products." Algebraic & Geometric Topology 20, no. 1 (February 23, 2020): 215–38. http://dx.doi.org/10.2140/agt.2020.20.215.

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26

Agrawal, Sunil K., Saravana Kumar, and Mark Yim. "Polyhedral Single Degree-of-freedom Expanding Structures: Design and Prototypes." Journal of Mechanical Design 124, no. 3 (August 6, 2002): 473–78. http://dx.doi.org/10.1115/1.1480413.

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Some engineering applications require structures to expand and contract in size, while retaining their exterior shape. The applications range from mundane daily life objects to more fancy art structures. In contrast to a multi degree-of-freedom structure, a single degree-of-freedom structure can be driven by a single actuator, reducing cost and simplifying the control. In this paper, we study single degree-of-freedom structures that can be formed by a lattice of single degree-of-freedom polyhedral expanding units. Due to built-in symmetries, the entire structure can expand and contract as one of the units in the structure is actuated. The paper describes the design of polyhedral single degree-of-freedom systems, the structures of their dynamics/optimal control, and results from construction prototypes.

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27

Huzyak, Paige, John Ferguson, Jeremiah Sharpensteen, Lan Xu, Soundaram Jeevarathinam Ananthakrishnan, and Hemali Rathnayake. "Fused arene-functionalized polyhedral oligomeric silsesquioxanes as thermoelectric materials." RSC Advances 5, no. 47 (2015): 37859–68. http://dx.doi.org/10.1039/c5ra00183h.

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Two derivatives of fused-arene functionalized polyhedral oligomeric silsesquioxanes (POSS-ANT and POSS-PDI-POSS) were synthesized and their electronic properties were studied for organic-based thermoelectric devices.

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Jover Biboum, Margarita, Rubén García Rubio, and Carlos Ávila Calzada. "Adrian Parr, a polyhedral relationship with water." ZARCH, no. 15 (January 27, 2021): 188–95. http://dx.doi.org/10.26754/ojs_zarch/zarch.2020154932.

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Adrian Parr is a transdisciplinary scholar who brings the design disciplines into conversation with the humanities, social sciences, and science. Rather than work within the clearly defined boundaries of a specialized discipline, her writings and movies create ethical montages consisting of theoretical criticism, poetics, imagery, and sound. The daughter and niece of two of Australia's most well-known contemporary artists, she has a sensitivity toward the affective potential of thought and ethical reflection. Her writings encompass a journey through the notebooks of Leonardo da Vinci, Deleuze, feminism, contemporary art, sustainability culture, urbanism, climate change, policy, collective memory, trauma theory, and Marxist thinking. Her films set out to humanize the water and sanitation statistics driving national and international policy. In this interview Adrian Parr talks about the environmental and water problems in different parts of the world under a vision in which humanism, education, ethics, awareness and leadership play a transcendental role.

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He, Huiwen, Hao Zheng, Meng Ma, Yanqing Shi, Zengliang Gao, Si Chen, and Xu Wang. "Peripheral groups of polyhedral oligomeric silsesquioxane (POSS) core-based dendrimers: a crucial factor for higher-level supra-architecture building." Nanoscale 12, no. 22 (2020): 12146–53. http://dx.doi.org/10.1039/d0nr03216f.

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Peripheral groups of polyhedral oligomeric silsequioxane based dendrimers act as the crucial factor in unique loofah-like gel superstructures construction via controlling the hierarchical self-assembly in a thermodynamics approach.

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Pitchanathan, Arjun, Christian Ulmann, Michel Weber, Torsten Hoefler, and Tobias Grosser. "FPL: fast Presburger arithmetic through transprecision." Proceedings of the ACM on Programming Languages 5, OOPSLA (October 20, 2021): 1–26. http://dx.doi.org/10.1145/3485539.

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Presburger arithmetic provides the mathematical core for the polyhedral compilation techniques that drive analytical cache models, loop optimization for ML and HPC, formal verification, and even hardware design. Polyhedral compilation is widely regarded as being slow due to the potentially high computational cost of the underlying Presburger libraries. Researchers typically use these libraries as powerful black-box tools, but the perceived internal complexity of these libraries, caused by the use of C as the implementation language and a focus on end-user-facing documentation, holds back broader performance-optimization efforts. With FPL, we introduce a new library for Presburger arithmetic built from the ground up in modern C++. We carefully document its internal algorithmic foundations, use lightweight C++ data structures to minimize memory management costs, and deploy transprecision computing across the entire library to effectively exploit machine integers and vector instructions. On a newly-developed comprehensive benchmark suite for Presburger arithmetic, we show a 5.4x speedup in total runtime over the state-of-the-art library isl in its default configuration and 3.6x over a variant of isl optimized with element-wise transprecision computing. We expect that the availability of a well-documented and fast Presburger library will accelerate the adoption of polyhedral compilation techniques in production compilers.

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Kajikawa, Yasushi. "Transitions in the Topology of Polyhedra." Leonardo 26, no. 1 (1993): 57. http://dx.doi.org/10.2307/1575782.

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32

Hart, George. "Mind-blowing modular origami: the art of polyhedral paper folding, by Byriah Loper." Journal of Mathematics and the Arts 11, no. 3 (July 3, 2017): 180–86. http://dx.doi.org/10.1080/17513472.2017.1368129.

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33

Kausar, Ayesha, and Patrizia Bocchetta. "Poly(methyl methacrylate) Nanocomposite Foams Reinforced with Carbon and Inorganic Nanoparticles—State-of-the-Art." Journal of Composites Science 6, no. 5 (April 28, 2022): 129. http://dx.doi.org/10.3390/jcs6050129.

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Polymeric nanocomposite foams have attracted increasing research attention for technical reasons. Poly(methyl methacrylate) is a remarkable and viable thermoplastic polymer. This review highlights some indispensable aspects of poly(methyl methacrylate) nanocomposite foams with nanocarbon nanofillers (carbon nanotube, graphene, etc.) and inorganic nanoparticles (nanoclay, polyhedral oligomeric silsesquioxane, silica, etc.). The design and physical properties of poly(methyl methacrylate) nanocomposite foams have been deliberated. It has been observed that processing strategies, nanofiller dispersion, and interfacial interactions in poly(methyl methacrylate)–nanofiller have been found essential to produce high-performance nanocellular foams. The emergent application areas of the poly(methyl methacrylate) nanocomposite foams are electromagnetic interference shielding, sensors, and supercapacitors.

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34

Sudbery, Anthony. "Dürer's magic tesseract." Mathematical Gazette 97, no. 538 (March 2013): 8–12. http://dx.doi.org/10.1017/s0025557200005374.

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Albrecht Dürer's mysterious engraving Melencolia I (Figure 1) has always intrigued both art critics and mathematicians. Among art critics, according to Campbell Dodgson [1], “The literature on the Melancholia is more extensive than that on any other engraving by Dürer” (he adds “the statement would probably remain true if the last two words were omitted”). Mathematicians, if disconcerted by the association between mathematics and melancholy, have been fascinated by the objects appearing in the print, such as the polyhedron occurring on the left of the engraving and—the subject of this note—the magic square in the upper right-hand corner (Figure 2).

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Uylaş Satı, Nur, and Burak Ordin. "Application of the Polyhedral Conic Functions Method in the Text Classification and Comparative Analysis." Scientific Programming 2018 (June 28, 2018): 1–11. http://dx.doi.org/10.1155/2018/5349284.

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In direct proportion to the heavy increase of online information data, the attention to text categorization (classification) has also increased. In text categorization problem, namely, text classification, the goal is to classify the documents into predefined classes (categories or labels). Recently various methods in data mining have been experienced for text classification in literature except polyhedral conic function (PCF) methods. In this paper, PCFs are used to classify the documents. The separation algorithms via PCFs which include linear programming subproblems with inequality constraints are presented. Numerical experiments are done on real-world text datasets. Comparisons are made between state-of-the-art methods by presenting obtained tenfold cross-validation results, accuracy values, and running times in tables. The results verify that in text classification PCF methods are as effective in terms of accuracy values as state-of-the-art methods.

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Guo, Hao, Aiping Wu, Ying Xie, Haijing Yan, Dongxu Wang, Lei Wang, and Chungui Tian. "2D porous molybdenum nitride/cobalt nitride heterojunction nanosheets with interfacial electron redistribution for effective electrocatalytic overall water splitting." Journal of Materials Chemistry A 9, no. 13 (2021): 8620–29. http://dx.doi.org/10.1039/d0ta11997k.

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Porous 2D Mo₂N-Co_xN heterojunction nanosheets have been constructed based on a new strategy of cutting ZIF-67 polyhedral in Na₂MoO₄ aqueous solution. The material can act effective bi-functional catalysts for overall water splitting.

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Taube, Karl A. "Obsidian Polyhedral Cores and Prismatic Blades in the Writing and Art of Ancient Mexico." Ancient Mesoamerica 2, no. 01 (March 1991): 61–70. http://dx.doi.org/10.1017/s0956536100000377.

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Hart, George W. "In the Palm of Leonardo’s Hand: Modeling Polyhedra." Nexus Network Journal 4, no. 2 (November 2002): 103–12. http://dx.doi.org/10.1007/s00004-002-0018-0.

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Rollings, Robert Weadon. "Polyhedra expressed through the beauty of wood." Journal of Mathematics and the Arts 4, no. 4 (December 2010): 191–99. http://dx.doi.org/10.1080/17513472.2010.487182.

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Kaduk, James A. "Tribarium dicitrate pentahydrate, [Ba3(C6H5O7)2(H2O)4]·H2O." Acta Crystallographica Section E Crystallographic Communications 77, no. 3 (February 12, 2021): 251–54. http://dx.doi.org/10.1107/s2056989021001407.

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The crystal structure of tribarium dicitrate pentahydrate, [Ba3(C6H5O7)2(H2O)4]·H2O, has been solved and refined using synchrotron X-ray powder diffraction data, and optimized using density functional techniques. The BaO9 and BaO10 coordination polyhedra share edges and corners to form a three-dimensional network. All of the active hydrogen atoms act as donors in O—H...O hydrogen bonds. Most of the acceptors are carboxylate oxygen atoms, but there are also water...water hydrogen bonds. Both of the citrate hydroxyl groups form intramolecular O—H...O hydrogen bonds to terminal carboxyl groups.

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Hermita, Neni, Zetra Hainul Putra, Jesi Alexander Alim, Jianlan Tang, Tommy Tanu Wijaya, Li Li, Jerito Pereira, and Maximus Tamur. "The Hungry Ant: Development of Video-Based Learning on Polyhedron." International Journal of Interactive Mobile Technologies (iJIM) 15, no. 17 (September 6, 2021): 18. http://dx.doi.org/10.3991/ijim.v15i17.23099.

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This research on learning media development is to answer the challenge of using technology in this 21st century wherein technology is growing rapidly. The purpose of this research is to develop a learning media in the form of learning video on primary school topics. Researchers chose polyhedron to be the research subject. This search will use the 4D model and will only focus from the define up to the development stage. While the small-scale try-out and disseminate of the learning video can be done in another research. According to the validation result, the hungry ant video passed the validation and only needed a few revisions. The hungry ant video would be able to help students to visualize the shape of polyhedron, finding the diagonal space, proofing the area and volume formulas. Future research can analyze effect of the hungry ant video towards the students’ critical thinking ability.

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Gee, Andrew H., and Richard W. Prager. "Polyhedral Combinatorics and Neural Networks." Neural Computation 6, no. 1 (January 1994): 161–80. http://dx.doi.org/10.1162/neco.1994.6.1.161.

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The often disappointing performance of optimizing neural networks can be partly attributed to the rather ad hoc manner in which problems are mapped onto them for solution. In this paper a rigorous mapping is described for quadratic 0-1 programming problems with linear equality and inequality constraints, this being the most general class of problem such networks can solve. The problem's constraints define a polyhedron P containing all the valid solution points, and the mapping guarantees strict confinement of the network's state vector to P. However, forcing convergence to a 0-1 point within P is shown to be generally intractable, rendering the Hopfield and similar models inapplicable to the vast majority of problems. A modification of the tabu learning technique is presented as a more coherent approach to general problem solving with neural networks. When tested on a collection of knapsack problems, the modified dynamics produced some very encouraging results.

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Glicksman, Martin E., Paulo Rangel Rios, and Daniel Lewis. "Kinetics of a Grain in a Textured Matrix." Materials Science Forum 558-559 (October 2007): 625–32. http://dx.doi.org/10.4028/www.scientific.net/msf.558-559.625.

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The multiplicity and variety of grain shapes in three-dimensional polycrystalline metals makes their energetic and kinetic analyses difficult. To help simplify the analysis of isotropic polycrystals, average N-hedra (ANHs) (N=3,4,5,…∞) were created as a set of regular polyhedra, consisting of N identical faces, which act as topological “proxies” for analyzing the corresponding class of irregular grains containing mixed faces of the same number. This paper outlines a further generalization of the ANH concept that extends three-dimensional analysis to include the growth or shrinkage of a small population of grains embedded in a textured matrix.

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Zhou, Li, Fang, Zhao, Wang, Zhang, and Zhou. "MOF-Derived Co3O4 Polyhedrons as Efficient Polysulfides Barrier on Polyimide Separators for High Temperature Lithium–sulfur Batteries." Nanomaterials 9, no. 11 (November 6, 2019): 1574. http://dx.doi.org/10.3390/nano9111574.

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The incorporation of highly polarized inorganic compounds in functional separators is expected to alleviate the high temperature safety- and performance-related issues for promising lithium–sulfur batteries. In this work, a unique Co3O4 polyhedral coating on thermal-stable polyimide (PI) separators was developed by a simple one-step low-temperature calcination method utilizing metal-organic framework (MOF) of Co-based zeolitic-imidazolate frameworks (ZIF-Co) precursors. The unique Co3O4 polyhedral structures possess several structural merits including small primary particle size, large pore size, rich grain boundary, and high ionic conductivity, which endow the ability to adequately adsorb dissolved polysulfides. The flexible-rigid lithium-lanthanum-zirconium oxide-poly(ethylene oxide) (LLZO-PEO) coating has been designed on another side of the polyimide non-woven membranes to inhibit the growth of lithium dendrites. As a result, the as-fabricated Co3O4/polyimide/LLZO-PEO (Co3O4/PI/LLZO) composite separators displayed fair dimensional stability, good mechanical strength, flame retardant properties, and excellent ionic conductivity. More encouragingly, the separator coating of Co3O4 polyhedrons endows Li–S cells with unprecedented high temperature properties (tested at 80 °C), including rate performance 620 mAh g−1 at 4.0 C and cycling stability of 800 mAh g−1 after 200 cycles—much better than the state-of-the-art results. This work will encourage more research on the separator engineering for high temperature operation.

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Goemans, Onno C., and A. Frank van der Stappen. "On the design of traps for feeding 3D parts on vibratory tracks." Robotica 26, no. 4 (July 2008): 537–50. http://dx.doi.org/10.1017/s0263574707004079.

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SUMMARYIn the context of automated feeding (orienting) of industrial parts, we study the algorithmic design of traps in the bowl feeder track that filter out all but one orientation of a given polyhedral part. We propose a new class of traps that removes a V-shaped portion of the track. The proposed work advances the state-of-the-art in algorithmic trap design by extending earlier work1,6,17—which focuses solely on 2D parts—to 3D parts, and by incorporating a more realistic part motion model in the design algorithm. We exploit the geometric structure of the design problem and build on concepts and techniques from computational geometry to obtain an efficient algorithm that reports the complete set of valid traps.

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Yakubovich, Olga, Galina Kiriukhina, Polina Verchenko, Sergey Simonov, Anatoly Volkov, and Olga Dimitrova. "Na-Alternative to Tinsleyite Obtained under Hydrothermal Conditions: Crystal Structure and Comparative Crystal Chemistry." Minerals 12, no. 5 (April 27, 2022): 542. http://dx.doi.org/10.3390/min12050542.

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The synthesis and characterization of a new aluminophosphate, Na2Al2O(PO4)2·0.12H2O obtained as single crystals, is reported. Centrosymmetric tetramers built from AlO5 polyhedra sharing edges and vertices, represent the distinguished feature of the compound. These tetrameric units of AlO5 bipyramids are cross-linked by PO4 tetrahedra to form two-periodic slabs alternating with Na+ ions and a small amount of H2O molecules. The Na2Al2O(PO4)2·0.12H2O with an original crystal architecture is chemically and structurally related to the mineral tinsleyite, KAl2(PO4)2(OH)·2H2O. Similar clusters of Al-centered polyhedra are essential building blocks of both monoclinic structures. The main difference between them consists of the type of the Al coordination by O atoms: in tinsleyite, the clusters are designed from AlO4(OH)2 and AlO4(OH)(H2O) octahedra. In both cases, alkali Na or K atoms significantly distinct in size, act as structure regulating agents, determining the character of the developing crystal architecture. The flexibility of aluminophosphate constructions allows them to self-organize around structure-forming Na+ or K+ ions into anionic layers in Na2Al2O(PO4)2·0.12H2O or a framework (tinsleyite). The synthesis of sodium aluminophosphate under mild hydrothermal conditions and the topological resemblance of its structure with that of the mineral tinsleyite suggest a high probability of a mineral equivalent of the Na2Al2O(PO4)2·0.12H2O in nature.

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Zhang, Zi-Mou, Peng-Cheng Gao, Zhi-Fei Wang, Bai-Wang Sun, and Yong Jiang. "DNA-caged gold nanoparticles for controlled release of doxorubicin triggered by a DNA enzyme and pH." Chemical Communications 51, no. 65 (2015): 12996–99. http://dx.doi.org/10.1039/c5cc05164a.

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DNA polyhedron-caged AuNPs were self-assembled using four-point-star DNAs, with three strands hybridizing to each other and the fourth strand attaching to the AuNPs. The caged AuNPs can act as doxorubicin nanocarriers; a DNA enzyme and pH can trigger controlled release.

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Glicksman, Martin E. "Capillarity-Mediated Grain Growth in 3-D." Materials Science Forum 467-470 (October 2004): 1025–32. http://dx.doi.org/10.4028/www.scientific.net/msf.467-470.1025.

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Space-filling in kinetically active 3-d network structures, such as polycrystalline solids at high temperatures, is treated using topological methods. The theory developed represents individual network elements—the polyhedral cells or grains—as a set of objects called average N-hedra, where N, the topological class, equals the number of contacting neighbors in the network. Average N-hedra satisfy network topological averages for the dihedral angles and quadrajunction vertex angles, and, most importantly, act as “proxies” for real irregular polyhedral grains with equivalent topology. The analysis provided in this paper describes the energetics and kinetics of grains represented as average N-hedra as a function of their topological class. The new approach provides a quantitative basis for constructing more accurate models of three-dimensional grain growth. As shown, the availability of rigorous mathematical relations for the curvatures, areas, volumes, free energies, and rates of volume change provides precise predictions to test simulations of the behavior 3-d networks, and to guide quantitative experiments on microstructure evolution in three-dimensional polycrystals.

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Várkonyi, Péter L., Márton Kocsis, and Tamás Ther. "Rigid impacts of three-dimensional rocking structures." Nonlinear Dynamics 107, no. 3 (December 30, 2021): 1839–58. http://dx.doi.org/10.1007/s11071-021-06934-x.

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AbstractStudies of rocking motion aim to explain the remarkable earthquake resistance of rocking structures. State-of-the-art assessment methods are mostly based on planar models, despite ongoing efforts to understand the significance of three-dimensionality. Impacts are essential components of rocking motion. We present experimental measurements of free-rocking blocks on a rigid surface, focusing on extreme sensitivity of impacts to geometric imperfections, unpredictability, and the emergence of three-dimensional motion via spontaneous symmetry breaking. These results inspire the development of new impact models of three-dimensional facet and edge impacts of polyhedral objects. Our model is a natural generalization of existing planar models based on the seminal work of George W. Housner. Model parameters are estimated empirically for rectangular blocks. Finally, new perspectives in earthquake assessment of rocking structures are discussed.

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Kearton, Cherry, and Vitaliy Kurlin. "All 2–dimensional links in 4–space live inside a universal 3–dimensional polyhedron." Algebraic & Geometric Topology 8, no. 3 (July 26, 2008): 1223–47. http://dx.doi.org/10.2140/agt.2008.8.1223.

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