Knots in Art by Radmila Sazdanović, Ana Zeković, Ljiljana Radović, Slavik Jablan

“…We propose different methods for generating knots and links based on geometric polyhedra, suitable for applications in architecture and sculpture.…”
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Polyhedral Graphs of GRAPH PARTITIONING and COMPLETE BIPARTITE SUBGRAPH Problems by A. I. Antonov, V. A. Bondarenko

“…<p>We provide an effective description of graphs of polyhedra for GRAPH PARTITIONING and COMPLETE BIPARTITE SUBGRAPH problems. …”
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Continuous Flattening of a Regular Tetrahedron with Explicit Mappings by Jin-ichi Itoh, Chie Nara

“…We proved in [10] that each Platonic polyhedron P can be folded into a flat multilayered face of P by a continuous folding process of polyhedra. In this paper, we give explicit formulas of continuous functions for such a continuous flattening process in R³ for a regular tetrahedron.The article is published in the author’s wording.…”
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Digital measurements of non-metallic inclusions in steel by Natalia A. Stukalova, Davronjon F. Kodirov, Valeriy I. Alekseev, Elina A. Sokolovskaya, Irina G. Rodionova

“…When representing the NMI as a set of random points on the plane, the distribution of distances between the nearest ones is estimated based on Voronoi polyhedra statistics. The study shows that an increase in the kurtosis coefficient of distributions of polyhedra areas is accompanied by an increase in the corrosion rate of the steels under study. …”
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Positive and Negative Contribution from Lead–Oxygen Groups and Halogen Atoms to Birefringence: A First Principles Investigation by Can Deng, Jialong Wang, Mei Hu, Xiuhua Cui, Haiming Duan, Peng Li, Ming-Hsien Lee

“…The contribution of atoms and polyhedra to birefringence was further evaluated using the Born effective charge. …”
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An orthorhombic polymorph of cerium(III) ultraphosphate, CeP5O14 by Jing Zhu, Wen-Dan Cheng, Hao Zhang

“…The structure contains (P5O14)3&#8722; anionic ribbons linked by distorted CeO8 polyhedra.…”
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Delaunay Meshing of Piecewise Smooth Complexes without Expensive Predicates by Tamal K. Dey, Joshua A. Levine

“…Recently a Delaunay refinement algorithm has been proposed that can mesh piecewise smooth complexes which include polyhedra, smooth and piecewise smooth surfaces, and non-manifolds. …”
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The first organically templated thorium compounds, [C4N2H12]0.5[ThF5] and [C5N2H14][ThF6].0.5H2O. by Kim, J, Norquist, A, O'Hare, D

“…Organically templated thorium compounds were synthesized for the first time under hydrothermal conditions; the piperazine containing compound consists of 2-D layers, while the 2-methylpiperazine phase contains unprecedented 1-D chains of face-sharing ThF9 polyhedra.…”

A digital Jordan surface theorem with respect to a graph connectedness by Šlapal Josef

“…These are obtained as polyhedral surfaces bounding the polyhedra that can be face-to-face tiled with digital tetrahedra.…”
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Complementarity and Preorganisation in the Assembly of Heterometallic–Organic Cages via the Metalloligand Approach—Recent Advances by Feng Li, Leonard F. Lindoy

“…The design of new metallocage polyhedra towards pre-determined structures can offer both practical as well as intellectual challenges. …”
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Cation substitution and strain screening in framework structures: The role of rigid unit modes by Goodwin, A, Wells, SA, Dove, M

“…We show that the geometric stress associated with the substitution in these framework silicates is absorbed by rigid-unit type motion of those coordination polyhedra near the substitution site. We find that the inherent flexibility of these structures enables screening of geometric stress, such that the associated energy cost is minimal and unlikely to influence substitution patterns. © 2005 Elsevier B.V. …”

Duality Between the Webs of Heterotic and Type II Vacua by Candelas, P, Font, A

“…We observe that perturbative symmetry restoration, as well as non-perturbative processes such as changes in the number of tensor multiplets, have at least in many cases a simple description in terms of the reflexive polyhedra of the Calabi-Yau manifolds. Our results suggest that to many, perhaps all, four-dimensional N=2 heterotic vacua there are corresponding type II vacua.…”

From nanoscale heterogeneities to nanolites: cation clustering in glasses by Cormier, Laurent, Galoisy, Laurence, Lelong, Gérald, Calas, Georges

“…The structural characteristics of these Zr- or Fe-rich clusters are similar, as both are based on edge-sharing cation polyhedra. Cations may also occur in a network-forming position. …”
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Changes of the slab structure of constitution scandate SrLaScO4 at the isovalent substitution of strontium atoms by Y.A.Titov, N.M. Belyavina, M.S.Slobodyanik, V.V.Chumak

“…Blocks are separated by the slab of (Sr, Ca, La)О9 polyhedra. Analysis of the obtained data has shown that, in a case of the substitution of Sr atoms by Ca atoms in SPS of Sr1–xCaxLaScO4, a gradual reduction of the length of the (Sr, Ca, La) — О2 interblock bond and the increases of the deformation degree (Δ) of interblock (Sr,Ca,La)О9 polyhedra and the mutual inclination of octahedrons ScO6 take place. …”
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Terbium(III) hydrogendiphosphate(V) tetrahydrate by Michal Du&#353;ek, Brahim El Bali, Rachid Essehli, Karla Fejfarov&#225;

“…The Tb atom of the title compound, TbHP2O7&#183;4H2O, is coordinated by the O atoms of three symmetrically independent water molecules and by five O atoms belonging to HP2O7&#8722; groups. The TbO8 polyhedra are interconnected by the diphospate anions, forming a three-dimensional network which is additionally stabilized by O&#8212;H...O hydrogen bonding between water molecules and O atoms of the HP2O7&#8722; anions. …”
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Ru11Lu20, a New Intermetallic Compound with Eight- to Ten-Coordinate Ruthenium Atoms by Sina Zimmermann, Ingo Pantenburg, Gerd Meyer

“…Ruthenium atoms center eight-, nine- and ten-vertex polyhedra of lutetium atoms which are connected in a complicated manner to a three-dimensional network.…”
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Planetary Systems and the Hidden Symmetries of the Kepler Problem by József Cseh

“…He could not prove his expectation, inasmuch as the planetary orbits are not transformed into each other by the regular polyhedra. In 1989, Barut proposed another relation, which was inspired by the hidden symmetry of the Kepler problem. …”
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Spatial Planning: A Configuration Space Approach by Lozano-Perez, Tomas

“…The paper presents algorithms for computing these Configuration Space obstacles when the objects and obstacles are polygons or polyhedra. An approximation technique for high-dimensional Configuration Space obstacles, based on projections of obstacles slices, is described.…”
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Generating Semantic Descriptions From Drawings of Scenes With Shadows by Waltz, David L.

“…The computer programs involved look at scenes which consist of polyhedra and which may contain shadows and various kinds of coincidentally aligned scene features. …”
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On the Monniaux Problem in abstract interpretation by Fijalkow, N, Lefaucheux, E, Ohlmann, P, Ouaknine, J, Pouly, A, Worrell, J

“…In this paper, we show that the Monniaux Problem is undecidable for unguarded affine programs and semilinear invariants (unions of polyhedra). Moreover, we show that decidability is recovered in the important special case of simple linear loops. …”