A second triclinic polymorph of bis(μ-N-nitroso-N-phenylhydroxylaminato)-κ3O,O′:O′;κ3O′:O,O′-bis[(N-nitroso-N-phe... by Ezzatollah Najafi, Mostafa M. Amini, Seik Weng Ng

“…The geometries of the five-coordinate PbII atoms in the two independent molecules are Ψ-octahedral; if more remote Pb...O interactions are also considered, the coordination number is increased to six for one molecule and to seven for the other. Their coordination polyhedra are ill defined in the chain motif, which runs along [100].…”
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Rerefinement of the crystal structure of α-ThBr4 by Tim Graubner, Florian Kraus

“…The connectivity of these polyhedra is 3∞[ThBr4/2Br4/2]. In comparison with the previous crystal structure refinement [Mason et al. (1974). …”
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Differential contracting homotopy in higher-spin theory by M. A. Vasiliev

“…Remarkably, the problem of reconstruction of higher-spin vertices is mapped to certain polyhedra cohomology in terms of homotopy parameters themselves. …”
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H-type Ce2[Si2O7] by Ralf Jules Christian Locke, Maria Weis, Thomas Schleid

“…The four crystallographically distinct CeIII cations form distorted square antiprisms, capped square antiprisms, and bicapped square antiprisms as coordination polyhedra consisting of oxygen atoms. Four crystallographically different silicon atoms recruit the centers of two different isolated [Si2O7]6– units.…”
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Redetermination of Ba2CdTe3 from single-crystal X-ray data by Min Yang, Sheng-Qing Xia, Xu-Tang Tao

“…The two Ba2+ cations are located between the chains, both within distorted monocapped trigonal–prismatic coordination polyhedra. All atoms in the structure are located on a mirror plane.…”
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The Form and Function of Duality in Modern Mathematics by Ralf Krömer, David Corfield

“…Phenomena covered by the term duality occur throughout the history of mathematics in all of its branches, from the duality of polyhedra to Langlands duality. By looking to an “internal epistemology” of duality, we try to understand the gains mathematicians have found in exploiting dual situations. …”
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Shedding Light on Shadows by Waltz, David L.

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Generating Semantic Description from Drawings of Scenes with Shadows by Waltz, David L.

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Model-Based Recognition and Localization from Sparse Range or Tactile Data by Grimson, W. Eric L., Lozano-Perez, Tomas

“…The objects are modeled as polyhedra having up to six degrees of freedom relative to the sensors. …”
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Computer Recognition of Three-Dimensional Objects in a Visual Scene by Guzman-Arenas, Adolfo

“…The input is a two-dimensional line-drawing of the scene, assumed to contain three-dimensional bodies possessing flat faces (polyhedra); some of them may be partially occluded. …”
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TiO2 nanocages : fast synthesis, interior functionalization and improved lithium storage properties by Wang, Zhiyu, Lou, David Xiong Wen

“…High-quality anatase TiO2 nanocages with anisotropic shapes, homogeneous shells and tunable sizes can be fabricated by templating against Cu2O polyhedra under hydrothermal conditions. The interiors of these TiO2 nanocages can be functionalized easily with Au nanoparticles. …”
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Soft cells and the geometry of seashells by Domokos, G, Goriely, A, Horváth, ÁG, Regős, K

“…The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp corners and flat faces. …”

Open-framework germanates - A study of nets and tilings by Bonneau, C, Shi, L, Christensen, K, Tang, L, Zou, X

“…Most of them were built from a few types of inorganic clusters containing a well-defined number of polyhedra: Ge3O9 (4=1), Ge4O16 (D4R) and larger clusters including 7, 9 and 10 Ge atoms (named Ge7, Ge9, Ge10 clusters, respectively). …”

Growing and characterizing one-dimensional crystals within single-walled carbon nanotubes. by Hutchison, J, Sloan, J, Kirkland, A, Green, M

“…ThCl4 was found to form a chain structure of Th[Cl]8 polyhedra. HgI2 crystallized within nanotubes with ultra-narrow (i.e. 0.8 nm) capillaries was observed to form helical 2 x 1 layer crystals.…”

POSSIBLE SYMMETRIES OF FULLERENE STRUCTURES by Fowler, P, Manolopoulos, D, Redmond, D, Ryan, R

“…Fullerene polyhedra are realisable within exactly 28 point groups: Ih, I, Td, Th, T, Dnh, Dnd, Dn (n=2, 3, 5, 6), S2m, Cmh, Cmv, Cm (m=2, 3), Cs, Ci, C1. …”

Synthesis and structural chemistry of La18Li8Rh4MO39 (M=Ti, Mn, Ru) by Battle, P, Dutton, SE, van Daesdonk, P

“…These channels are occupied by chains made up of alternating, face-sharing trigonal-prismatic and octahedral coordination polyhedra; there are two crystallographically distinct types of octahedral site. …”

Negative thermal expansion in ZrW2O8: Mechanisms, rigid unit modes, and neutron total scattering by Tucker, MG, Goodwin, A, Dove, M, Keen, D, Wells, SA, Evans, J

“…We obtain, for the first time, quantitative measurements of the extent to which the WO4 and ZrO6 polyhedra move as rigid units, and we show that these values are consistent with the predictions of rigid unit mode theory. …”

Toric Hyperkahler Varieties by Hausel, T, Sturmfels, B

“…Extending work of Bielawski-Dancer and Konno, we develop a theory of toric hyperkahler varieties, which involves toric geometry, matroid theory and convex polyhedra. The framework is a detailed study of semi-projective toric varieties, meaning GIT quotients of affine spaces by torus actions, and specifically, of Lawrence toric varieties, meaning GIT quotients of even-dimensional affine spaces by symplectic torus actions. …”

The vibrational motion of 'polymeric' BeCl2 by Wilson, M, Ribeiro, M

“…The dangers of assigning experimental bands in terms of the motions of local coordination polyhedra are emphasized. © 1999 Taylor and Francis Ltd.…”

Design of three-dimensional open-framework structures from inorganic clusters by Christensen, K, Shi, L, Tang, L, Conradsson, T, Dadachov, MS, Zou, X

“…Their structures were built from a single or two types of inorganic clusters containing a number of well-defined Ge-O coordination polyhedra. Different arrangements and combinations of these clusters resulted in different open-framework structures including some germanate/silicogermanates with extra-large pores (16- 24 rings). …”